Economic Models - Convex Optimization

ECONOMIC MODELS
Methods, Theory
and Applications

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ECONOMIC MODELS
Methods, Theory
and Applications
editor
Dipak Basu
Nagasaki University, Japan
World Scientific
N E W J E R S E Y • L O N D O N • S I N G A P O R E • B E I J I N G • S H A N G H A I • H O N G K O N G • TA I P E I • C H E N N A I

Published by
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ECONOMIC MODELS
Methods, Theory and Applications
Copyright © 2009 by World Scientific Publishing Co. Pte. Ltd.
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This Volume is Dedicated to the Memory of
Prof. Tom Oskar Martin Kronsjo

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Contents
Tom Oskar Martin Kronsjo: A Profile
About the Editor
Contributors
Introduction
Chapter 1: Methods of Modelling: Mathematical
Programming
Topic 1: Some Unresolved Problems of Mathematical
Programming
by Olav Bjerkholt
ix
xiii
xv
xix
1
3
Chapter 2: Methods of Modeling: Econometrics
and Adaptive Control System
21
Topic 1: A Novel Method of Estimation Under Co-Integration 23
by Alexis Lazaridis
Topic 2: Time Varying Responses of Output to Monetary
and Fiscal Policy
by Dipak R. Basu and Alexis Lazaridis
43
Chapter 3: Mathematical Modeling in Macroeconomics 67
Topic 1: The Advantages of Fiscal Leadership in an Economy
with Independent Monetary Policies
by Andrew Hughes Hallet
Topic 2: Cheap-Talk Multiple Equilibria and Pareto —
Improvement in an Environmental Taxation Games
by Chirstophe Deissenberg and Pavel Ševčík
69
101
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viii
Contents
Chapter 4: Modeling Business Organization 119
Topic 1: Enterprise Modeling and Integration: Review
and New Directions
by Nikitas Spiros Koutsoukis
Topic 2: Toward a Theory of Japanese Organizational Culture
and Corporate Performance
by Victoria Miroshnik
121
137
Topic 3: Health Service Management Using Goal Programming 151
by Anna-Maria Mouza
Chapter 5: Modeling National Economies 171
Topic 1: Inflation Control in Central and Eastern European
Countries
by Fabrizio Iacone and Renzo Orsi
Topic 2: Credit and Income: Co-Integration Dynamics
of the US Economy
by Athanasios Athanasenas
173
201
Index 223

Tom Oskar Martin Kronsjo: A Profile
Lydia Kronsjo
University of Birmingham, England
Tom Kronsjo was born in Stockholm, Sweden, on 16 August 1932, the
only child of Elvira and Erik Kronsjo. Both his parents were gymnasium
teachers.
In his school days Tom Kronsjo was a bright, popular student, often
a leader among his school contemporaries and friends. During his school
years, he organized and chaired a National Science Society that became
very popular with his school colleagues.
From an early age, Tom Kronsjo’s mother encouraged him to learn
foreign languages. He put these studies to a good test during a 1948 summer
vacation when he hitch-hiked through Denmark, Germany, the Netherlands,
England, Scotland, Ireland, France, and Switzerland. The same year Tom
Kronsjo founded and chaired a technical society in his school. In the summer
vacation of 1949, Tom Kronsjo organized an expedition to North Africa
by seven members of the technical society, their ages being 14–24. The
young people traveled by coach through the austere post-Second World War
Europe. All the equipment for travel, including the coach, were donated
by sympathetic individuals and companies, who were impressed by an
intelligent, enthusiastic group of youngsters, eager to learn about the world.
This event caught a wide interest in the Swedish press at that time and was
vividly reported.
Tom Kronsjo used to mention that as a particularly personally exciting
experience of his school years he remembered volunteering to give a series
of morning school sermons on the need for the world governmental organizations,
which would encourage and support mutual understanding of the
needs of the people to live in peace.
Tom Kronsjo’s university years were spent at both sides of the great
divide. Preparing himself for a career in international economics, he wanted
to experience and see for himself the different nations’ ways of life and
points of view. He studied in London, Belgrade,Warsaw, Oslo, and Moscow,
before returning to his home country, Sweden, to pass examinations and
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x
Tom Oskar Martin Kronsjo
submit required work at the Universities of Uppsala, Stockholm and Lund
for his Fil.kand. degree in economics, statistics, mathematics and Slavonic
Languages, and Fil.lic. degree in economics. By then, Tom Kronsjo besides
his mother tongue — Swedish, was fluent in six languages — German,
English, French, Polish, Serbo-Croatian, and Russian. During this period,
Tom was awarded a number of scholarships for study in Sweden and abroad.
Tom Kronsjo met his wife while studying in Moscow. He was a visiting
graduate student at the Moscow State University and she a graduate student
with the Academy of Sciences of the USSR. They married in Moscow in
February 1962. A few years later, a very happy event in the family life was
the arrival of their adoptive son from Korea in October 1973.
As a post-graduate student in economics, Tom Kronsjo was one of a
new breed of Western social scientists that applied rigorous mathematical
and computer-based modeling to economics. In 1963, Tom Kronsjo was
invited by Professor Ragnar Frish, later Nobel prize winner in econometrics,
to work under him and Dr. Salah Hamid in Egypt as a visiting Assistant
Professor in Operations Research at the UAR Institute of National Planning.
His pioneering papers on optimization of foreign trade were soon
considered classic and brought invitations to work as a guest researcher by
the GDR Ministry of Foreign Trade and Inner German Trade, and by the
Polish Ministry of Foreign Trade.
In 1964, Tom Kronsjo was appointed an Associate Professor in Econometrics
and Social statistics at the Faculty of Commerce and Social Sciences,
the University of Birmingham, U.K. He and his wife moved to the
United Kingdom.
In Birmingham, together with Professor R.W. Davies Tom Kronsjo
developed diploma, and master of social sciences courses in national economic
planning. The courses, offered from 1967, attracted many talented
students from all over the world. Many of these students then stayed
with Tom Kronsjo as research students and many of these people are
today university professors, industrialists, and economic advisors. In 1969,
at the age of 36, Tom Kronsjo was appointed Professor of Economic
Planning. By then Tom Kronsjo had published over a hundred research
papers.
Tom Kronsjo has always had a strong interest in educational innovations.
He was among the first professors at the university to introduce a
television-based teaching, making it possible to widen the scope of material
taught.
Tom Kronsjo was generous towards his students with his research ideas,
stimulating his students intellectually, unlocking wide opportunities for his

Tom Oskar Martin Kronsjo
students through this generosity. He had the ability to see the possibilities
in any situation and taught his students to use them.
Tom Kronsjo’s research interests were wide and multifaceted. One
area of his interest was planning and management at various levels of
the national economy. He developed important methods of decomposition
of large economic systems, which were considered by his contemporaries
a major contribution to the theory of mathematical planning and
programming. These results were published in 1972 in a book “Economics
of Foreign Trade” written jointly by Tom Kronsjo, Dr. Z. Zawada, and
Professor J. Krynicki, both of the Warsaw University, and published in
Poland.
In 1972, Tom Kronsjo was invited as a Visiting Professor of Economics
and Industrial Administration at Purdue University, Purdue, USA.
In 1974, Tom Kronsjo was a Distinguished Visiting Professor of Economics,
at San Diego State University, San Diego, USA.
In the year 1975, Tom Kronsjo found himself as a Senior Fellow in the
Foreign Policy Studies Program of the Brookings Institution, Washington,
D.C., USA. In collaboration with three other scientists, he was engaged
in the project entitled “Trade and Employment Effects of the Multilateral
Trade Negotiations”. In the words of his colleagues, Tom Kronsjo made an
indispensable contribution to the project. Tom Kronsjo’s ingenious, tireless,
conceptual, and implementing efforts made it possible to carry out
calculations involving millions of pieces of information on trade and tariffs,
permitting the Brookings model to become the most sophisticated and comprehensive
model available at the time for investigation into effects of the
current multilateral trade negotiations. In addition, Tom Kronsjo conceived
and designed the means for implementing, perhaps the most imaginative
portion of the project, the calculation of “optimal” tariff cutting formulas
using linear programming and taking account of balance of payments and
other constraints on trade liberalization. A monograph on “Trade, Welfare,
and Employment Effects of Trade Negotiations in the Tokyo Round” by
Dr. W.R. Cline, Dr. Noboru Kawanabe, Tom Kronsjo, and T. Williams was
published in 1978.
Tom Kronsjo’s general interests have been in the field of conflicts and
co-operation, war and peace, ways out of the arms race, East-West joint
enterprises and world development. He published papers on unemployment,
work incentives, and nuclear disarmament.
Tom Kronsjo served as one of the five examiners for one of the Nobel
prizes in economic sciences. From time to time, he was invited to nominate
a candidate or candidates for the Nobel prize in economics.
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Tom Oskar Martin Kronsjo
Tom Kronsjo took early retirement from the University of Birmingham
in 1988 and devoted subsequent years working with young researchers from
China, Russia, Poland, Estonia, and other countries.
Tom Kronsjo was a great enthusiast of vegetarianism and veganism,
of Buddhist philosophy, yoga, and inter-space communication, of aviation
and flying. He learned to fly in the United States and held a pilot license
since 1972.
Tom Kronsjo was a man who lived his life to the fullest, who constantly
looked for ways to bring peace to the world. He was an exceptional individual
who had the incredible vision and an ability to foresee new trends.
He was a man of great charisma, one of those people of whom we say “he
is a man larger than life”.
Tom Oskar Martin Kronsjo died in June 2005 at the age of 72.

About the Editor
Prof. Dipak Basu is currently a Professor in International Economics in
Nagasaki University in Japan. He has obtained his Ph.D. from the University
of Birmingham, England and did his post-doctoral research in Cambridge
University. He was previously a Lecturer in Oxford University — Institute
of Agricultural Economics, Senior Economist in the Ministry of Foreign
Affairs, Saudi Arabia and Senior Economist in charge of Middle East &
Africa Division of Standard & Poor (Data Resources Inc). He has published
six books and more than 60 research papers in leading academic journals.
xiii

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Contributors
Athanasios Athanasenas is an Assistant Professor of Operations Research
& Economic Development in the School of Administration & Economics,
Institute of Technology and Education, Serres, Greece. He was educated in
Colorado and Virginia Universities and received his Ph.D. from the University
of Minnesota. He was a Full-Bright scholar.
Olav Bjerkholt, Professor in Economics, University of Oslo, was previously
the Head of the Research at the Norwegian Statistical Office and an
Assistant Professor of Energy Economics at the University of Oslo. He has
obtained his Ph.D. from the University of Oslo. He was a Visiting Professor
in the Massachusetts Institute of Technology and was a consultant to the
United Nations and the IMF.
Christophe Deissenberg is a Professor in Economics, at Université dela
Méditerranée and GREQAM, France. He is a co-editor of the Journal of
Optimization Theory and Applications and of Macroeconomic Dynamics,
a member of the editorial board of Computational Economics and of Computational
Management Science. He is a member of the Advisory Board of
the Society for Computational Economics and a member of the Management
Committee of the ESF action COSTP10–Physics of Risk, and a team
leader of the European STREP project EURACE.
Andrew Hughes Hallett is a Professor of Economics and Public Policy
in the School of Public Policy at George Mason University, USA. Previously
he was a Professor of Economics at Vanderbilt University, and the
University of Strathclyde in Glasgow, Scotland. He was educated in the
University of Warwick and London School of Economics, holds a doctorate
from Oxford University. He was a Visiting Professor in Princeton
University, Free University of Berlin, Universities of Warwick, Frankfurt,
Rome, Paris X and in the Copenhagen Business School. He is a Fellow of
the Royal Society of Edinburgh.
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xvi
Contributors
Fabrizio Iacone obtained a Ph.D. in Economics at the London School of
Economics and is currently a Lecturer in the Department of Economics at
the University of York, UK. He has already published several articles in
leading journals.
Nikos Konidaris is currently a Ph.D. student at Hellenic Open University,
School of Social Sciences, researching in the field of Business Administration.
He holds an MA degree in Business and Management and a Bachelor’s
Degree in Economics & Marketing from Luton University UK.
Nikitas Spiros Koutsoukis is anAssistant Professor of Decision Modelling
and Scientific Management in the Department of International Economic
Relations and Development, Democritus University, Greece. He holds MSc
and Ph.D. in decision modeling from Brunel University (UK). He is interested
mainly in decision modeling and governance systems, with applications
in risk management, business intelligence and operational research
based decision support.
Alexis Lazaridis, Professor in Econometrics, Aristotle University of Thessaloniki,
Greece, has obtained his Ph.D. from the University of Birmingham,
England. He was a member of the Administrative Board of the Organization
of Mediation and Arbitration, of the Administrative Board of the
Centre of International and European Economic Law, and of the Supreme
Labour Council of Greece. During his term of service as Head of the Economic
Department Faculty of Law and Economics, Aristotle University of
Thessaloniki, he was conferred an honorary doctoral degree by the President
of the Republic of Cyprus. He was also pronounced an honorary
member of the Centre of International and Economic European Law by the
Secretary-General of the Legal Services of E.U. He has published several
books, large number of scientific papers and has patents on two computer
software programs.
Athanassios Mihiotis is an Assistant Professor at the School of Social
Science of the Hellenic Open University. He has obtained his Ph.D. in
industrial management from the National Technical University of Athens,
Greece. He is the editor of the International Journal of Decision Sciences,
Risk and Management. He has in the past worked as Planning and Logistics
Director for multinational and domestic companies and has served as
member of project teams in the Greek public sector.

Contributors
Victoria Miroshnik, is currently anAdam Smith Research Scholar, Faculty
of Law and Social Sciences, University of Glasgow, Scotland. She was
educated in Moscow State University and was an Assistant Professor in
Tbilisi State University, Georgia. She has published two books and a large
number of scientific papers in leading management journals.
Anna-Maria Mouza, Assistant Professor in Business Administration,
Technological Educational Institute of Serres, Greece, has obtained her
Ph.D. from the School of Health Sciences, Aristotle University of
Thessaloniki, Greece. Previously, she was an Assistant Professor in the
School of Technology Applications of the Technological Institute of
Thessaloniki, in the Department of Agriculture and in the Faculty of Health
Sciences of the Aristotle University of Thessaloniki. She is the author of
two books and many published scientific papers.
R. Orsi, Professor in Econometrics, University of Bologna, Italy, has
obtained his Ph.D. from Universitè Catholique de Louvain, Belgium. He
was previously educated in the University of Bologna and in the University
of Rome. He was an Associate Professor in the University of Modena, and
Professor of Econometrics in the University of Calabria, Italy. He was a
Visiting Professor in the Center for Operation Research and Econometrics
(CORE), Universitè-Catholique de Louvain, Belgium, Nato Senior Fellow,
Head of the Department of Economics at the University of Calabria
from 1987 to 1989, Director of CIDE (the Inter-Universitary Center of
Econometrics) from 1997 to1999, and from 2000 to 2002, and the Head of
Department of Economics, University of Bologna from 1999 to 2002.
Pavel Ševčík, was educated in the Université delaMéditerranée. He is
presently completing his Ph.D in the Universilé de Montréal, Canada.
xvii

Introduction
We define “model building in economics,” as the fruitful area of economics
designed to solve real-world problems using all available methods available
without distinctions: mathematical, computational, and analytical.
Wherever needed we should not be shy to develop new techniques —
whether mathematical or computational. This was the philosophy of Prof
Tom Kronsjo, in whose memory we dedicate this volume. The idea is to
develop stylized facts amenable to analytical methods to solve problems of
the world.
The articles in this volume are divided into three distinct groups: methods,
theory, and applications.
In the method section there are two parts: mathematical programming
and computation of co-integrating vectors, which are widely used in econometric
analysis. Both these parts are important to analyze and develop policies
in any analytical model. Berjkholt has reviewed the history of development
of mathematical programming and its impacts in economic modeling.
In the process, he has drawn our attention to some methods, first developed
by Ragner Frisch, which can provide solution where the standard Simplex
method may fail. Frisch has developed these methods while working on the
Second Five Year’s Plan for India and has developed a method, which is
similar to that of Karmarkar.
Lazaridis presents a completely new method to compute co-integration
vectors, widely used in econometric analysis, by applying singular value
decomposition. With this method, one can easily accommodate in the cointegrating
vectors any deterministic factors, such as dummies, apart from
the constant term and the trend. In addition, a comparatively simple procedure
is developed for determining the order of integration of a different stationary
series. Besides, with this procedure one can directly detect whether
the differencing process produces a stationary series or not, since it seems
to be a common belief that differencing a variable (one or more times) we
will always get a stationary series, although this is not necessarily the case.
Basu and Lazaridis have proposed a new method of estimation and
solution of an econometric model with parameters moving over time. This
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xx
Introduction
type of model is very realistic for economies, which are in transitional
phases. The model was applied for the Indian economy to derive monetaryfiscal
policy structure that would respond to the changing environments of
the economy. The authors provide analysis to show that the response of the
economy would be variable i.e., not at all fixed over time.
In the macroeconomic theory section Hughes-Hallet has examined the
impacts of fiscal policy in a regime with independent monetary authority
and how to co-ordinate public policies in such a regime. Independence
of the central bank is a crucial issue for both developed and developing
country. In this theoretical model, the author has discovered some important
conclusions that fiscal leadership leads to improved outcomes because it
implies a degree of co-ordination and reduced conflicts between institutions,
without the central bank having to lose its ability to act independently.
Deissenberg and Pavel consider a dynamic model of environmental
taxation that exhibits time inconsistency. There are two categories of firms,
believers (who take the non-binding tax announcements made by the regulator
at face value), and non-believers (who make rational but costly predictions
of the true regulator’s decisions). The proportion of believers and
non-believers changes over time depending on the relative profits of both
groups. If the regulator is sufficiently patient and if the firms react sufficiently
fast to the profit differences, multiple equilibria can arise. Depending
on the initial number of believers, the regulator will use cheap-talk together
with actual taxes to steer the economy either to the standard, perfect prediction
solution suggested in the literature, or to equilibrium with a mixed
population of believers and non-believers who both make prediction errors.
This model can be very useful in the analysis of environmental economics.
In the section on theory of business organization, Victoria Miroshnik
has formulated a model of Japanese organization and how the superior
corporate performances in the Japanese multi-national companies are the
result of a multi-layer structure of cultures, national, personal, organizational.
The model goes deep into the analysis of fundamental ingredient of
Japanese organizational culture and human resource management system
and how these contribute to corporate performance. The model produces a
novel scheme, how to estimate phenomena which are seemingly unobserved
psychological and sociological characteristics.
Mihiotis et al., discussed enterprise modeling and integration challenges,
and rationale as well as current tools and methodology for deeper
analysis. Over the last decades, much has been written and a lot of research
has been undertaken on the issue of enterprise modeling and integration.
The purpose of this discussion is to provide an overview and understanding

Introduction
of the key concepts. The authors have outlined a framework for advancing
enterprise integration modeling based on the state-of-the art techniques.
Anna Maria Mauza in a path breaking research presents a model suitable
for an efficient budget management of a health service unit, by applying goal
programming. She analyzes all the details needed to formulate the proper
model, in order to successfully apply goal programming, in an attempt to
satisfy the expectations of the decision maker in the best possible way,
providing at the same time alternative scenarios considering various socioeconomic
factors.
In the section for policy analysis, Iacone and Orsi applied a small macroeconometric
model to ascertain if the inflation dynamics and controls for
Poland, Czech Republic, and Slovenia, are compatible with the remaining
EU member countries. They found that the real exchange rate is the most
effective instrument to stabilize inflation whereas direct inflation control
mechanisms may be ineffective in certain cases. These experiments are
very useful to design anti-inflation policies in open economies.
AthanasiosAthanasenas investigated the co-integration dynamics of the
credit–income nexus, within the economic growth process of the post-war
US economy, over the period from 1957 up to 2007. Given the existing
empirical research on the credit-lending channel and the established relationship
between financial intermediation and economic growth in general,
the main purpose is to analyze in detail the causal relationship between
finance and growth by focusing on bank credit and income GNP, in the
post-war US economy. This is a new application of an innovative technique
of co-integration analysis with emphasis on system stability analysis. The
results show that there is no short-run effect of credit changes on income
changes, but only in the long-run, credit affects money income.
The book covers most of the important areas of economics with the basic
analytical framework to formulate a logical structure and then suggest and
implement methods to quantify the structure to derive applicable policies.
We hope the book would be a source of joy for anyone interested to make
economics a useful discipline to enhance human welfare rather than being
a sterile discourse devoid of reality.
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Chapter 1
Methods of Modelling: Mathematical
Programming

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Topic 1
Some Unresolved Problems of Mathematical
Programming
Olav Bjerkholt
University of Oslo, Norway
1. Introduction
Linear programming (LP) emerged in the United States in the early postwar
years. One may to a considerable degree see the development of LP
as a direct result of the mobilization of research efforts during the war.
George B. Dantzig, who was employed by the US Armed Forces, played a
key role in developing the new tool by his discovery in 1947 of the Simplex
method for solving LP problems. Linear programming was thus a military
product, which soon appeared to have very widespread civilian applications.
The US Armed Forces continued its support of Dantzig’s LP work, as the
most widespread textbook in LP in the 1960s, namely Dantzig (1963), was
sponsored by the US Air Force.
Linear programming emerged at the same time as the first electronic
computers were developed. The uses and improvements in LP as an optimization
tool developed in step with the fast development of electronic
computers.
A standard formulation of a LP problem in n variables is as follows:
min{c ′ x |Ax = b, x ≥ 0}
x
where c ∈ R n , b ∈ R m and A a (m, n) matrix of rank m

4 Olav Bjerkholt
Among these was also Ragnar Frisch. Frisch was broadly oriented towards
macroeconomic policy and planning problems and was highly interested
in the promising new optimization tool. Frisch, who had a strong background
in mathematics and also was very proficient in numerical methods,
made the development of solution algorithms for LP problems a part of his
research agenda. During the 1950s, Frisch invented and tested out various
solution algorithms along other lines than the Simplex method for solving
LP problems.
With regard to the magnitude of LP problems that could be solved
at different times with the computer equipment at disposal, Orden (1993)
gives the following rough indication. In the first year after 1950, the number
m of constraints in a solvable problem was of order 100 and has grown
with a factor of 10 for each decade, implying that currently LP problems
may have a number of constraints that runs into tens of millions. Linear
programming has been steadily taken into use for new kinds of problems
and the computer development has allowed the problems to be bigger and
bigger.
The Simplex method has throughout this period been the dominant
algorithm for solving LP problems, not least in the textbooks. It is perhaps
relatively rare that an algorithm developed at an early stage for new problem,
as Dantzig did with the Simplex method for the LP problem, has retained
such a position. The Simplex method will surely survive in textbook presentations
and for its historical role, but for the solution of large-scale LP
problems it is yielding ground to alternative algorithms. Ragnar Frisch’s
work on algorithms is interesting in this perspective and has been given
little attention. It may on a modest scale be a case of a pioneering effort
that was more insightful than considered at the time and thus did not get
the attention it deserved. In the history of science, there are surely many
such cases.
Let us first make a remark on the meaning of algorithms. The mathematical
meaning of “algorithm” in relation to a given type of problem is a
procedure, which after finite number of steps finds the solution to the problem,
or determines that there is no solution. Such an algorithmic procedure
can be executed by a computer program, an idea that goes back to Alan
Turing. But when we talk about algorithms with regard to the LP problem
it is not in the mathematical sense, but a more practical one. An LP
algorithm is a practically executable technique for finding the solution to
the problem. Dantzig’s Simplex method is an algorithm in both meanings.
But one may have an algorithm in the mathematical sense, which is not a
practical algorithm (and indeed also vice versa).

Some Unresolved Problems 5
In the mathematical sense of algorithm, the LP problem is trivial. It
can easily be shown that the feasibility region is a convex set with a linear
surface. The optimum point of a linear criterion over such a set must be in a
corner or possibly in a linear manifold of dimension greater than one.As the
number of corners is finite, the solution can be found, for example, by setting
n − m of the x’s equal to zero and solve Ax = b for the remaining ones.
Then all the corners can be searched for the lowest value of the optimality
criterion.
Dantzig (1984) gives a beautiful illustration of why such a search for
optimality is not viable. He takes a classical assignment problem, the distribution
of a given number of jobs among the same number of workers.
Assume that 70 persons shall be assigned to 70 jobs and the return of each
worker-job combination is known. There are thus 70! possible assignment
combinations. Dantzig’s comment about the possibility of looking at all
these combinations runs as follows:
“Now 70! is a big number, greater than 10 100 . Suppose we had an IBM
370-168 available at the time of the big bang 15 billion years ago. Would
it have been able to look at all the 70! combinations by the year 1981?
No! Suppose instead it could examine 1 billion assignments per second?
The answer is still no. Even if the earth were filled with such computers
all working in parallel, the answer would still be no. If, however, there
were 10 50 earths or 10 44 suns all filled with nano-second speed computers
all programmed in parallel from the time of the big bang until sun grows
cold, then perhaps the answer is yes.” (Dantzig, 1984, p. 106)
In view of these enormous combinatorial possibilities, the Simplex
method is a most impressive tool by making the just mentioned and even
bigger problems practically solvable. The Simplex method is to search for
the optimum on the surface of the feasible region, or, more precisely, in the
corners of the feasible region, in such a way that the optimality criterion
improves at each step.
A completely different strategy to search for the optimum is to search
the interior of the feasible region and approach the optimal corner (or one of
them) from within, so to speak. It may seem to speak for the advantage of the
Simplex method that it searches an area where the solution is known to be.
A watershed in the history of LP took place in 1984 when Narendra
Karmarkar’s algorithm was presented at a conference (Karmarkar, 1984a)
and published later the same year in a slightly revised version (Karmarkar,
1984b). Karmarkar’s algorithm, which the New York Times found worthy
as first page news as a great scientific breakthrough, is such an “interior”

6 Olav Bjerkholt
method, searching the interior of the feasibility area in the direction of the
optimal point.
This idea had, however, been pursued by Ragnar Frisch. To the best of
my knowledge this was first noted by Roger Koenker a few years ago:
“But it is an interesting irony, illustrating the spasmodic progress of science,
that the most fruitful practical formulation of the interior point revolution
of Karmarkar (1984) can be traced back to a series of Oslo working
papers by Ragnar Frisch in the early 1950s.” (Koenker, 2000).
2. Linear Programming in Economics
Linear programming has a somewhat curious relationship with academic
economics. Few would today consider LP as a part of economic science. But
LP was, so to say, launched within economics, or even within econometrics,
and given much attention by leading economists for about 10 years or so.
After around 1960, the ties to economics were severed. Linear programming
disappeared from the economics curriculum and lost the attention of
academic economists. It belonged from then on to operations research and
management science on one hand and to computer science on the other.
It is hardly possible to answer to give an exact date for when “LP”
was born or first appeared. It originated at around the same time as game
theory with which it shares some features, and also at the time of some
applied problems such as the transportation problem and the diet problem.
Linear programming has various roots and forerunners in economics and
mathematics in attempts to deal with economic or other problems using
linear mathematical techniques. One such forerunner, but only slightly, was
Wassily Leontief’s input-output analysis. Leontief developed his “closed
model” in the 1930s in an attempt to give empirical content to Walrasian
general equilibrium. Leontief’s equilibrium approach was transformed in
his cooperation with the US Bureau of Labor Statistics to the open inputoutput
model, see Kohli (2001).
In the early post-war years, LP and input-output analysis seemed within
economics to be two sides of the same coin. The two terms were, for
a short term, even used interchangeably. The origin of LP could be set
to 1947, which, as already mentioned, was when Dantzig developed the
Simplex algorithm. If we state the question as to when “LP” was first
used in its current meaning in the title of a paper presented at a scientific
meeting, the answer is to the best of my knowledge 1948. At
the Econometric Society meeting in Cleveland at the end of December

Some Unresolved Problems 7
1948, Leonid Hurwicz presented a paper on LP and the theory of optimal
behavior with the first paragraph providing a concise definition for
economists:
“The term linear programming is used to denote a problem of a type
familiar to economists: maximization (or minimization) under restrictions.
What distinguishes linear programming from other problems in
this class is that both the function to be maximized and the restrictions
(equalities or inequalities) are linear in the variables.” (Hurwicz, 1949).
Hurwicz’s paper appeared in a session on LP, which must have been
the first ever with that title. One of the other two papers in the session was
by Wood and Dantzig and discussed the problem of selecting the “best”
method of accomplishing any given set of objectives within given restriction
as a LP problem, using an airlift operation as an illustrative example. The
general model was presented as an “elaboration of Leontief’s input-output
model.”
At an earlier meeting of the Econometric Society in 1948, Dantzig had
presented the general idea of LP in a symposium on game theory. Koopmans
had, at the same meeting, presented his general activity analysis production
model. The conference papers of both Wood and Dantzig appeared in
Econometrica in 1949. Dantzig (1949) mentioned as examples of problems
for which the new technique could be used, Stigler (1945), known in the
literature as having introduced the “diet problem,” and a paper by Koopmans
on the “transportation problem,” presented at an Econometric Society
meeting in 1947 (Koopmans, 1948).
Dantzig (1949) stated the LP problem, not yet in standard format, but the
solution technique was not discussed. The paper referred not only Leontief’s
input-output model but also to John von Neumann’s work on economic equilibrium
growth, i.e., to recent papers firmly within the realm of economics.
Wood and Dantzig (1949) in the same issue stated an airlift problem.
In 1949, Cowles Commission and RAND jointly arranged a conference
on LP. The conference meant a breakthrough for the new optimization
technique and had prominent participation. At the conference were
economists, Tjalling Koopmans, Paul Samuelson, Kenneth Arrow, Leonid
Hurwicz, Robert Dorfman, Abba Lerner and Nicholas Georgescu-Roegen,
mathematicians, Al Tucker, Harold Kuhn and David Gale, and several military
researchers including Dantzig.
Dantzig had discovered the Simplex method but admitted many years
later that he had not really realized how important this discovery was. Few
people had a proper overview of linear models to place the new discovery in

8 Olav Bjerkholt
context, but one of the few was John von Neumann, at the time an authority
on a wide range of problems form nuclear physics to the development
of computers. Dantzig decided to consult him about his work on solution
techniques for the LP problem:
“I decided to consult with the “great” Johnny von Neumann to see what
he could suggest in the way of solution techniques. He was considered
by many as the leading mathematician in the world. On October 3, 1947
I visited him for the first time at the Institute for Advanced Study at
Princeton. I remember trying to describe to von Neumann, as I would to
an ordinary mortal, the Air Force problem. I began with the formulation
of the linear programming model in terms of activities and items, etc. Von
Neumann did something, which I believe was uncharacteristic of him.
“Get to the point,” he said impatiently. Having at times a somewhat low
kindling point, I said to myself “O.K., if he wants a quicky, then that’s what
he’ll get.” In under one minute I slapped the geometric and the algebraic
version of the problem on the blackboard. Von Neumann stood up and
said “Oh that!” Then for the next hour and a half, he proceeded to give
me a lecture on the mathematical theory of linear programs.” (Dantzig,
1984).
Von Neumann could immediately recognize the core issue as he saw the
similarity with the game theory. The meeting became the first time Dantzig
heard about duality and Farkas’ lemma.
One could underline how LP once seemed firmly anchored in economics
by pointing to the number of Nobel Laureates in economics who
undertook studies involving LP. These comprise Samuelson and Solow, coauthors
with Dorfman of Dorfman, Samuelson and Solow (1958), Leontief
who applied LP in his input-output models, and Koopmans and Stigler,
originators of the transportation problem and the diet problem, respectively.
One also has to include Frisch, as we shall look at in more detail below,
Arrow, co-author of Arrow et al. (1958), Kantorovich, who is known to
have formulated the LP problem already in 1939, Modigliani, and Simon,
who both were co-authors of Holt et al. (1956). Finally, to be included
are also all the three Nobel Laureates in economics for 1990: Markowitz
et al. (1957), Charnes et al. (1959) and Sharpe (1967). Koopmans and
Kantorovich shared the Nobel Prize in economics for 1975 for their work
in LP. John von Neumann died long before the Nobel Prize in economics
was established, and George Dantzig never got the prize he ought to have
shared with Koopmans and Kantorovich in 1975 for reasons that are not
easy to understand.

Some Unresolved Problems 9
Among all these Nobel Laureates, it seems that Ragnar Frisch had the
deepest involvement with LP. But he published poorly and his achievements
went largely unrecognized.
3. Frisch and Programming, Pre-War Attempts
Ragnar Frisch had a strong mathematical background and a passion for
numerical analysis. He had been a co-founder of the Econometric Society
in 1930 and to him econometrics meant both the formulation of economic
theory in a precise way by means of mathematics and the development
of methods for confronting theory with empirical data. He wrote both
of these aims into the constitution of the Econometric Society as rendered
for many years in every issue of Econometrica. He became editor of
Econometrica from its first issue in 1933 and held this position for more than
20 years.
His impressive work in several fields of econometrics must be left
uncommented here. Frisch pioneered the use of matrix algebra in econometrics
in 1929 and had introduced many other innovations in the use of
mathematics for economic analysis.
Frisch’s most active and creative as a mathematical economist coincided
with the Great Depression, which he observed at close range both
in the United States and in Norway. In 1934, he published an article
in Econometrica (Frisch, 1934a) where he discussed the organization of
national exchange organization that could take over the need for trade
when markets had collapsed due to the depression, see Bjerkholt and Knell
(2006). In many ways, the article may seem naïve with regard to the subject
matter, but it had a very sophisticated mathematical underpinning.
The article was 93 pages long, the longest regular article ever published
in Econometrica. Frisch had also published the article without letting it
undergo proper referee process. Perhaps it was the urgency of getting it
circulated that caused him to do this mistake for which he was rebuked
by some of his fellow econometricians. The article was written as literally
squeezed in between Frisch two most famous econometric contributions
in the 1930s, his business cycle theory (Frisch, 1933) and his confluence
theory (Frisch, 1934b).
Frisch (1934a) developed a linear structure representing inputs for production
in different industries, rather similar to the input-output model
of Leontief, although the underlying idea and motivation was quite different.
Frisch then addressed the question of how the input needs could

10 Olav Bjerkholt
be modified in the least costly way in order to achieve a higher total
production capacity of the entire economy. The variables in his problem
(x i ) represented (relative) deviations from observed input coefficients.
He formulated a cost function as a quadratic function of these deviations.
His reasoning thus led to a quadratic target function to be minimized
subject to a set of linear constraints. The problem was stated as
follows:
[ ]
min = 1 x
2
1
+ x2 2
+···+ x2 n
wrt. x k k = 1, 2,...,n
2 ε 1 ε 2 ε n
subject to: k f ik x k ≥ C ∗ − a i0
i = 1,...,n
P i
where C ∗ is the set target of overall production and the constraint the condition
that the deviation allowed this target value to be achieved.
By solving for alternative values of C ∗ , the function = (C ∗ ),
representing the cost of achieving the production level C ∗ could be mapped.
Frisch naturally did not possess an algorithm for this problem. This did
not prevent him from working out a numerical solution of an illuminating
example and making various observations on the nature of such optimising
problems. His solution of the problem for a given example with n = 3,
determining as a function of C ∗ ran over 12 pages in Econometrica, see
Bjerkholt (2006).
Another problem Frisch worked on before the war with connections
to LP was the diet problem. One of Frisch’s students worked on a dissertation
on health and nutrition, drawing on various investigations of the
nutritional value of alternative diets. Frisch supervised the dissertation in
the years immediately before World War II when it led him to formulate
the diet problem, years before Stigler (1945). Frisch’s work was published
as the introduction to his student’s monograph (Frisch, 1941). In a footnote,
he gave a somewhat rudimentary LP formulation of the diet problem,
cf. Sandmo (1993).
4. Frisch and Linear Programming
Frisch was not present at the Econometric Society meetings in 1948 mentioned
above; neither did he participate in the Cowles Commission-RAND
conference in 1949. He could still survey and follow these developments
rather closely. He was still the editor of Econometrica and thus had accepted
and surely studied the two papers by Dantzig in 1949. He had contact with
Cowles Commission in Chicago, its two successive research directors in

Some Unresolved Problems 11
these years, Jacob Marschak and Tjalling Koopmans, and other leading
members of the Econometric Society. Frisch visited in the early post-war
years frequently in the United States, primarily due to his position as chairman
of the UN Sub-Commission for Employment and Economic Stability.
The new developments over the whole range of related areas of linear techniques
had surely caught his interest.
He first touched upon LP in lectures to his students at the University of
Oslo in September 1950. Two students drafted lecture notes that Frisch corroborated
and approved. In these early lectures Frisch used “input-output
analysis” and “LP” as almost synonymous concepts. The content of these
early lectures was input-output analysis with emphasis on optimisation by
means of LP, e.g., optimisation under a given import constraint or given
labor supply, they did not really address LP techniques as a separate issue.
Still these lectures may well have been among the first applying LP to
the macroeconomic problems of the day in Western Europe, years before
Dorfman et al. (1958) popularised this tool for economists’ benefit. One
major reason for Frisch pioneering efforts here was, of course, that the
new ideas touched or even overlapped with his own pre-war attempts as
discussed above. In the very first post-war years, he had indeed applied
the ideas of Frisch (1934a) to the problem of achieving the largest possible
multilateral balanced trade in the highly constrained world economy
(Frisch, 1947; 1948).
The first trace of LP as a topic in its own right on Frisch’s agenda
was a single lecture he gave to his students on February 15th 1952. Leif
Johansen, who was Frisch’s assistant at the time, took notes that were issued
in the Memorandum series two days later (Johansen, 1952). The lecture
gave a brief mathematical statement of the LP problem and then as an
important example discussed the problem related to producing different
qualities of airplane fuel from crude oil derivates, with reference to an
article by Charnes et al. in Econometrica. Charnes et al. (1952) is, indeed,
a famous contribution in the LP literature as the first published paper on
an industrial application of LP. A special thing about the Frisch’s use of
this example was, however, that his lecture did not refer the students to
an article that had already appeared in Econometrica, but to one that was
forthcoming! Frisch had apparently been so eager to present these ideas
that he had simply used (or perhaps misused) his editorial prerogative in
lecturing and issuing lecture notes on an article not yet published!
After the singular lecture on LP in February 1952, Frisch did not lecture
on this topic till the autumn term in 1953, as part of another lecture series
on input-output analysis. In these lectures, he went by way of introduction

12 Olav Bjerkholt
through a number of concrete examples of problem that were amenable to
be solved by LP, most of which have already been mentioned above. When
he came to the diet problem, it was not with reference to Stigler (1945), but
to Frisch (1941). He exemplified, not least, with reconstruction in Norway,
the building of dwellings under the tight post-war constraints and various
macroeconomic problems.
In his brief introduction to LP, Frisch in a splendid pedagogical way
used examples, amply illustrated with illuminating figures, and appealed to
geometric intuition. He started out with cost minimization of a potato and
herring diet with minimum requirements of fat, proteins and vitamin B, and
then moved to macroeconomic problems within an input-output framework,
somewhat similar in tenor to Dorfman (1958), still in the offing.
Frisch confined, however, his discussion to the formulation of the LP
problem and the characteristics of the solution, he did not enter into solution
techniques. But clearly he had already put considerable work into this.
Because after mentioning Dantzig’s Simplex method, referring to Dantzig
(1951), Dorfman (1951) and Charnes et al. (1953), he added that there
were two other methods, the logarithm potential method and the basis
variable method, both developed at the Institute of Economics. He added
the remark that when the number of constraints was moderate and thus the
number of degrees of freedom large, the Simplex method might well be
the most efficient one. But in other cases, the alternative methods would be
more efficient. Needless to say, there were no other sources, which referred
to these methods at this time. Frisch’s research work on LP methods and
alternatives to the Simplex method, can be followed almost step by step
thanks to his working style of incorporating new results in the Institute
Memorandum series. Between the middle of October 1953 and May 1954,
he issued 10 memoranda.They were all in Norwegian, but Frisch was clearly
preparing for presenting his work. As were to be expected Frisch’s work on
LP was sprinkled with new terms, some of them adapted from earlier works.
Some of the memoranda comprised comprehensive numerical experiments.
The memoranda were the following:
18 October 1953 Logaritmepotensialmetoden til løsning av lineære
programmeringsproblemer [The logarithm potential
method for solving LP problems], 11 pages.
7 November 1953 Litt analytisk geometri i flere dimensjoner [Some
multi-dimensional analytic geometry], 11 pages.

Some Unresolved Problems 13
(Continued )
13 November 1953 Substitumalutforming av logaritmepotensialmetoden til
løsning av lineære programmeringsproblemer
[Substitumal formulation of the logarithmic potential
method for solving LP problems], 3 pages.
14 January 1954 Notater i forbindelse med logaritmepotensialmetoden til
løsning av lineære programmeringsproblemer [Notes
in connection with the logarithmic potential method
for solving LP problems], 48 pages.
7 March 1954 Finalhopp og substitumalfølging ved lineær
programmering [Final jumps and moving along the
substitumal in LP], 8 pages.
29 March 1954 Trunkering som forberedelse til finalhopp ved lineær
programmering [Truncation as preparation for a final
jump in LP], 6 pages.
27 April 1954 Et 22-variables eksempel på anvendelse av
logaritmepotensialmetoden til løsning av lineære
programmeringsproblemer [A 22 variable example in
application of the logarithmic potential method for the
solution of LP problems].
1 May 1954 Basisvariabel-metoden til løsning av lineære
programmeringsproblemer [The basis-variable
method for solving LP problems], 21 pages.
5 May 1954 Simplex-metoden til løsning av lineære
programmeringsproblemer [The Simplex method for
solving LP problems], 14 pages.
7 May 1954 Generelle merknader om løsningsstrukturen ved det
lineære programmeringsproblem [Generfal remarks
on the solution structure of the LP problem],
12 pages.
At this stage, Frisch was ready to present his ideas internationally. This
happened first at a conference in Varenna in July 1954, subsequently issued
as a memorandum. During the summer, Frisch added another couple of
memoranda. Then he went to India, invited by Pandit Nehru, and spent the
entire academic year 1954–55 at the Indian Statistical Institute, directed
by P. C. Mahalanobis, to take part in the preparation of the new five-year
plan for India. While he was away, he sent home the MSS for three more

14 Olav Bjerkholt
memoranda. These six papers were the following:
June 21st 1954
August 13th 1954
August 23rd 1954
October 18th 1954
March 29th 1955
April 15th 1955
Methods of solving LP problems, Synopsis of lecture to be
given at the International Seminar on Input-Output
Analysis, Varenna (Lake Como), June–July 1954,
91 pages.
Nye notater i forbindelse med logaritmepotensialmetoden
til løsning av lineære programmeringsproblemer [New
notes in connection with the logarithmic potential
method for solving LP problems], 74 pages.
Merknad om formuleringen av det lineære
programmeringsproblem [A remark on the formulation of
the LP problem], 3 pages.
Principles of LP. With particular reference to the double
gradient form of the logarithmic potential method,
219 pages.
A labour saving method of performing freedom truncations
in international trade. Part I, 21 pages.
A labour saving method of performing freedom truncations
in international trade. Part II, 8 pages.
Before he left for India he had already accepted an invitation to present
his ideas on programming in Paris. This he did on three different occasions
in May–June 1955. He presented in French, but issued synopsis in English
in the memorandum series. Thus, his Paris presentation were the following:
7th May 1955 The logarithmic potential method for solving linear
programming problems, 16 pp. Synopsis of an exposition to
be made on 1 June 1955 in the seminar of Professor René
Roy, Paris (published as Frisch, 1956b).
13 May 1955 The logarithmic potential method of convex programming. With
particular application to the dynamics of planning for
national developments, 35 pp. Synopsis of a presentation to
be made at the international colloquium in Paris, 23–28 May
1955 (published as Frisch, 1956c).
25 May 1955 Linear and convex programming problems studied by means of
the double gradient form of the logarithmic potential method,
16pp. Synopsis of a presentation to be given in the seminar of
Professor Allais, Paris, 26 May 1955.

Some Unresolved Problems 15
After this, Frisch published some additional memoranda on LP. He
launched a new method, named the Multiplex method, towards the end of
1955, later published in a long article in Sankhya (Frisch, 1955; 1957).
Worth mentioning is also his contribution to the festschrift for Erik Lindahl
in which he discussed the logarithmic potential method and linked it to the
general problem of macroeconomic planning (Frisch, 1956a; 1956d).
From this time, Frisch’s efforts subsided with regard to pure LP problems,
as he concentrated on non-linear and more complex optimisation,
drawing naturally on the methods he had developed for LP.
As Frisch managed to publish his results only to a limited degree and
not very prominently there are few traces of Frisch in the international
literature. Dantzig (1963) has, however, references to Frisch’s work. Frisch
also corresponded with Dantzig, Charnes, von Neumann and others about
LP methods. Extracts from such correspondence are quoted in some of the
memoranda.
5. Frisch’s Radar: An Anticipation of Karmarkar’s Result
In 1972, severe doubts were created about the ability of the Simplex method
to solve even larger problems. Klee and Minty (1972), whom we must
assume knew very well how the Simplex algorithm worked, constructed
a LP problem, which when attacked by the Simplex method turned out
to need a number of elementary operations which grew exponentially in
the number of variables in the problem, i.e., the algorithm had exponential
complexity. Exponential complexity in the algorithm is for obvious reasons
a rather ruining property for attacking large problems.
In practice, however, the Simplex method did not seem to confront such
problems, but the demonstration of Klee and Minty (1972) showed a worst
case complexity, implying that it could never be proved what had been
largely assumed, namely that the Simplex method only had polynomial
complexity.
A response to Klee and Minty’s result came in 1978 by the Russian
mathematician Khachiyan 1978 (published in English in 1979 and 1980).
He used a so-called “ellipsoidal” method for solving the LP problem, a
method developed in the 1970s for solving convex optimisation problems by
the Russian mathematicians Shor and Yudin and Nemirovskii. Khachiyan
managed to prove that this method could indeed solve LP problems and
had polynomial complexity as the time needed to reach a solution increased
with the forth power of the size of the problem. But the method itself was

16 Olav Bjerkholt
hopelessly ineffective compared to the Simplex method and was in practice
never used for LP problems.
A few years later, Karmarkar presented his algorithm (Karmarkar,
1984a; b). It has polynomial complexity, not only of a lower degree than
Khachiyan’s method, but is asserted to be more effective than the Simplex
method. The news about Karmarkar’s path-breaking result became frontpage
news in the New York Times. For a while, there was some confusion as
to whether Karmarkar’s method really was more effective than the Simplex
method, partly because Karmarkar had used a somewhat special formulation
of the LP problem. But it was soon confirmed that for sufficently large
problems, the Simplex method was less effcient than Karmarkar’s result.
Karmarkar’s contribution initiated a hectic new development towards even
better methods.
Karmarkar’s approach may be said to be to consider the LP just as
another convex optimalization problem rather that exploiting the fact that
the solution must be found in a corner by searching only corner points. One
of those who has improved Karmarkar’s method, Clovis C. Gonzaga, and
for a while was in the lead with regard to possessing the nest method wrt.
polynomial complexity, said the following about Karmarkar’s approach:
“Karmarkar’s algorithm performs well by avoiding the boundary of the
feasible set. And it does this with the help of a classical resource, first
used in optimization by Frisch in 1955: the logarithmic barrier function:
x ∈ R n , x > 0 → p(x) =− ∑ log x i .
This function grows indefinitely near the boundary of the feasible set S,
and can be used as a penalty attached to these points. Combining p(·)
with the objective makes points near the boundary expensive, and forces
any minimization algorithm to avoid them.” (Gonzaga, 1992)
Gonzaga’s reference to Frisch was surprising; it was to the not very
accessible memorandum version in English of one of the three Paris papers. 1
Frisch had indeed introduced the logarithmic barrier function in his logarithmic
potential method. Frisch’s approach was summarized by Koenker
as follows:
“The basic idea of Frisch (1956b) was to replace the linear inequality
constraints of the LP, by what he called a log barrier, or potential function.
Thus, in place of the canonical linear program
1 In Gonzaga’s reference, the author’s name was given as K.R. Frisch, which can also be
found in other rerences to Frisch in recent literature, suggesting that these refrences had a
common source.

(1) min{c ′ x|Ax = b, x ≥ 0}
we may associate the logarithmic barrier reformulation
(2) min{B(x, µ)|Ax = b}
where
(3) B(x, µ) = c ′ x − µ ∑ log x k
Some Unresolved Problems 17
In effect, (2) replaces the inequality constraints in (1) by the penalty term
of the log barrier. Solving (2) with a sequence of parameters µ such that
µ → 0 we obtain in the limit a solution to the original problem (1).”
(Koenker, 2000, p. 20)
Frisch had not provided exact proofs and he had above all not published
properly. But he had the exact same idea as Karmarkar came up with almost
30 years later. Why did he not make his results better known? In fact there
are other, even more important cases, in Frisch’s work of not publishing. The
reasons for this might be that his investigations had not yet come to an end.
In the programming work Frisch pushed on to more complex programming
problems, spurred by the possibility of using first- and second-generation
computers. They might have seemed powerful to him at that time, but they
hardly had the capacity to match Frisch’s ambitions. Another reason for
his results remaining largely unknown, was perhaps that he was too much
ahead. The Simplex method had not really been challenged yet, by large
enough problems to necessitate better method. The problem may have seen,
not as much as a question of efficient algorithms as that of powerful enough
computers.
We finish off with Frisch’s nice illustrative description of his method in
the only publication he got properly published (but unfortunately not very
well distributed) on the logarithmic potential method:
“Ma méthode d’approche est d’une espèce toute différente. Dans cette
méthode nous travaillons systématiquement à l’intérieur de la région
admissible et utilisons un potentiel logarithmique comme un guide–
une sorte du radar–pour nous éviter de traverser la limite.” (Frisch,
1956b, p. 13)
The corresponding quote in the memorandum synoptic note is:
“My method of approach is of an entirely different sort [than the Simplex
method]. In this method we work systematically in the interior of the
admissible region and use a logarithmic potential as a guiding device — a
sort of radar — to prevent us from hitting the boundary.” (Memorandum
of 7 May 1955, p. 8)

18 Olav Bjerkholt
References
Arrow, KJ, L Hurwicz and H Uzawa (1958). Studies in Linear and Non-Linear Programming.
Stanford, CA: Stanford University Press.
Bjerkholt, O and M Knell (2006). Ragnar Frisch and input-output analysis. Economic
Systems Research 18, (forthcoming).
Charnes, A, WW Cooper and A Henderson (1953). An Introduction to Linear Programming.
New York and London: John Wiley & Sons.
Charnes, A, WW Cooper and B Mellon (1952). Bledning aviation gasolines — a study in
programming interdependent activities in an integrated oil company, Econometrica 20,
135–159.
Charnes, A, WW Cooper and MW Miller (1959). An application of linear programming to
financial budgeting and the costing of funds. The Journal of Business 20, 20–46.
Dantzig, GB (1949). Programming of interdependent activities: II mathematical model.
Econometrica 17, 200–211.
Dantzig, GB (1951). Maximization of a linear function of variables subject to linear inequalities.
In Activity Analysis of Production and Allocation, T Koopmans (ed.), New York
and London: John Wiley & Sons, pp. 339–347.
Dantzig, GB (1963). Linear Programming and Extensions. Princeton, NJ: Princeton
University Press.
Dantzig, GB (1984). Reminiscences about the origin of linear programming. In
Mathematical Programming, RW Cottle, ML Kelmanson and B Korte (eds.),
Amsterdam: Elsevier (North-Holland), pp. 217–226.
Dorfman, R (1951). An Application of Linear Programming to the Theory of the Firm.
Berkeley: University of California Press.
Dorfman, R, PA Samuelson and RM Solow, (1958). Linear Programming and Economic
Analysis. New York: McGraw-Hill.
Frisch, R (1933). Propagation problems and impulse problems in economics. In
Economic Essays in Honor of Gustav Cassel, R Frisch (ed.), London: Allen & Unwin,
pp. 171–205.
Frisch, R (1934a). Circulation planning: proposal for a national organization of a commodity
and service exchange. Econometrica 2, 258–336 and 422–435.
Frisch, R (1934b). Statistical Confluence Analysis by Means of Complete Regression
Systems. Publikasjon nr 5, Oslo: Institute of Economics.
Frisch, R (1941). Innledning. In Kosthold og levestandard. En økonomisk undersøkelse,
K Getz Wold (ed.), Oslo: Fabritius og Sønners Forlag, pp. 1–23.
Frisch, R (1947). On the need for forecasting a multilateral balance of payments. The American
Economic Review 37(1), 535–551.
Frisch, R (1948). The problem of multicompensatory trade. Outline of a system of multicompensatory
trade. The Review of Economics and Statistics 30, 265–271.
Frisch, R (1955). The multiplex method for linear programming. Memorandum from Institute
of Economics, Oslo: University of Oslo (17 October 1955).
Frisch, R (1956a). Macroeconomics and linear programming. Memorandum from Institute
of Economics, Oslo: University of Oslo, (10 January 1956). (Also published shortened
and simplified as Frisch (1956d)).
Frisch, R (1956b). La résolution des problèmes de programme linéaire par la méthode du
potential logarithmique. In Cahiers du Séminaire d’Econometrie: No4—Programme

Some Unresolved Problems 19
Linéaire — Agrégation et Nombre Indices, pp. 7–20. (The publication also gives an
extract of the oral discussion in René Roy’s seminar, pp. 20–23.)
Frisch, R (1956c). Programme convexe et planification pour le développement national.
Colloques Internationaux du Centre National de la Recherche Scientifique LXII. Les
modèles dynamiques. Conférence à Paris, mai 1955, 47–80.
Frisch, R (1956d). Macroeconomics and linear programming. In 25 Economic Essays. In
honour of Erik Lindahl 21 November 1956, R Frisch (ed.), pp. 38–67. Stockholm:
Ekonomisk Tidskrift, (Slightly simplified version of Frisch (1956a)).
Frisch, R (1957). The multiplex method for linear programming. Sankhyá: The Indian
Journal of Statistics 18, 329–362 [Practically identical to Frisch (1955)]
Gonzaga, CC (1992). Path-following methods for linear programming. SIAM Review 34,
167–224.
Holt, CC, F Modigliani, JF Muth and HA Simon (1956). Derivation of a linear decision rule
for production and employment. Management Science 2, 159–177.
Hurwicz, L (1949). Linear programming and general theory of optimal behaviour (abstract).
Econometrica 17, 161–162.
Johansen, L (1952). Lineær programming. (Notes from Professor Ragnar Frisch’s lecture
15 February 1952), pp. 15. Memorandum from Institute of Economics, University of
Oslo, 17 February 1952, 15pp.
Karmarkar, NK (1984). A new polynomial-time algorithm for linear programming. Combinatorica,
4, 373–395.
Klee, V and G Minty, (1972). How good is the simplex algorithm. In Inequalities III, O
Sisha (ed.), pp. 159–175. New York, NY: Academic Press.
Koenker, R (2000). Galton, Edgeworth, Frisch, and prospects for quantile regression in
econometrics. Journal of Econometrics, 95(2), 347–374.
Kohli, MC (2001). Leontief and the bureau of labor statistics, 1941–54: developing a
framework for measurement. In The Age of Economic Measurement, JL Klein and
MS Morgan (eds.), pp. 190–212. Durham and London: Duke University Press.
Koopmans, T (1948). Optimum utilization of the transportation system (abstract).
Econometrica 16, 66.
Koopmans, TC (ed.) (1951). Activity Analysis of Production and Allocation. Cowles
Commission Monographs No 13. New York: John Wiley & Sons.
Markowitz, H (1957). The elimination form of the inverse and its application in linear
programming. Management Science 3, 255–269.
Orden, A (1993). LP from the ’40s to the ’90s. Interfaces 23, 2–12.
Sandmo, A (1993). Ragnar Frisch on the optimal diet. History of Political Economy 25,
313–327.
Sharpe, W (1967). A linear programming algorithm for mutual fund portfolio selection.
Management Science 13, 499–511.
Stigler, G (1945). The cost of subsistence. Journal of Farm Economics 27, 303–314.
Wood, MK and GB Dantzig (1949). Programming of interdependent activities: I general
discussion. Econometrica 17, 193–199.

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Chapter 2
Methods of Modeling: Econometrics
and Adaptive Control System

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Topic 1
A Novel Method of Estimation
Under Co-Integration
Alexis Lazaridis
Aristotle University of Thessaloniki, Greece
1. Introduction
We start with the unrestricted VAR(p):
p∑
x i = δ + µt i + A j x i−j + zd i + w i (1)
j=1
where x ∈ E n (here, E denotes the Euclidean space), t i and d i are the
trend and dummy, respectively and w is the noise vector. The matrices of
coefficients A j , are defined on E n × E n . After estimation, we may compute
matrix from:
⎛ ⎞
p∑
= ⎝ A j
⎠ − I
(1a)
j=1
or, directly, from the corresponding Error CorrectionVAR (ECVAR), which
is presented later.Also, an estimate of matrix can be obtained by applying
OLS, according to the procedure suggested by Kleibergen and Van Dijk
(1994). It is re-called that this type of VAR models like the one presented
above, have been recommended by Sims (1980), as a way to estimate the
dynamic relationships among jointly endogenous variables.
It is known that matrix can be decomposed such that = AC,
where the elements of A are the coefficients of adjustment and the rows of
the matrix C are the (possible) co-integrating vectors. It should be clarified
at the very outset, that in many books etc., C is denoted by β ′ (prime shows
transposition) and A by α, although capital letters are used for denoting
matrices. Besides, in the general linear model, y = Xβ + u,β is the vector
of coefficients. To avoid any confusion, we adopted the notation used here.
23

24 Alexis Lazaridis
A straightforward approach to obtain matrices A and C, provided that
some rank conditions of are satisfied, is to solve the eigenproblem (Johnston
and Di Nardo, 1997, pp. 287–296).
= VV −1 (2)
where is the diagonal matrix of eigenvalues and V is the matrix of the
corresponding eigenvectors. Note that since is not symmetric, V ̸= V −1 .
Eq. (2) holds if is (n × n) and all its eigenvalues are real, which implies
that the eigenvectors are real too. In cases that is defined on E n × E m ,
with m>n, Eq. (2) is not applicable. If these necessary conditions hold,
then from Eq. (2) follows that matrix A = V and C = V −1 . Further, the
co-integrating vectors are normalized so that — usually — the first element
to be equal to 1. In other words, if c i 1 (̸=0), denotes the first element1 of
the ith row of matrix C, i.e., 2 c ′ i. and a j the jth column of matrix A, then
the normalization process can be summarized as c ′ i. /ci 1 and a i × c i 1 , for
i = 1,...,n.
It is known that according to the maximum likelihood (ML) method,
matrix C can be obtained by solving the constrained problem:
{min det(I − C ˆ k0 ˆ −1
00 ˆ 0k C ′ ) | C ˆ kk C ′ = I} (3)
where matrices ˆ 00 , ˆ 0k , ˆ kk and ˆ k0 are residual co-variance matrices of
specific regressions (Harris, 1995, p. 78; Johansen Juselius, 1990). These
matrices appear in the last term of the concentrated likelihood of 3 Eq. (5)
together with C, where is replaced by AC.
Note that the minimization of Eq. (3) is with respect to the elements
of matrix C. It is re-called that Eq. (3) is minimized by solving a general
eigenvalue problem, i.e., finding the eigenvalues from:
|λ ˆ kk − ˆ k0 ˆ −1
00 ˆ 0k |=0. (4)
Applying Cholesky’s factorization on the positive definite symmetric
matrix ˆ −1
kk , such that ˆ −1
kk = LL′ ⇒ ˆ kk = (L ′ ) −1 L −1 , where L is lower
1 In some computer programs, ci i is taken to be the ith element of the ith row.
2 Note that dot is necessary to distinguish the jth row of C, i.e., c i. ′ , from the transposed of
the jth column of this matrix (i.e., c i ′).
3 Equation (5) is presented below.

A Novel Method of Estimation Under Co-Integration 25
triangular, Eq. (4) takes the conventional form 4 :
|λI − L ′ ˆ k0 ˆ −1
00 ˆ 0k L|=0. (4a)
After obtaining matrix V = V ′ of the eigenvectors, we can easily
compute the (unormalized) C from C = V ′ L ′ . Note also that C ˆ kk C ′ =
V ′ L ′ (L ′ ) −1 L −1 LV = I. Finally, matrix A is obtained from A = ˆ 0k C ′ .
Hence, the initial problem reduces to finding one of the eigen values and
eigenvectors of a symmetric matrix, which are real. And this is the main
advantage of the ML method.According to this procedure, a constant and/or
trend can be included in the co-integrating vectors, but it is not clear of how
to accommodate additional deterministic factors, such as one or more dummies.
Besides, nothing is said about the variance of the (disequilibrium)
errors, which correspond to the finally adopted co-integration vector.
We propose in the first part of this chapter, a comparatively simple
method, to directly obtain co-integrating vectors, which may include, apart
from the standard deterministic components, any number of dummies, in
cases that this is necessary. Additionally, as we will see in what follows, the
errors corresponding to the proper co-integration vector have the property
of minimum variance.
2. Some Estimation Remarks
It was mentioned that after estimation, matrix can be computed from
Eq. (1a). It is obvious that each equation of the VAR can be estimated by
OLS. At this stage, one should be aware to comply with the basic assumptions
regarding the error terms, in the sense that proper tests must ensure
that the noises are white. This way, the order p of the model is defined
imposing at the same time restrictions — if necessary — on some elements
of A’s and vectors µ and z to be zero.
It can be easily shown that Eq. (1) may be expressed in the form of an
equivalent ECVAR, i.e.,
p−1
∑
x i = δ + µt i + Q j x i−j + x i−p + zd i + w i (5)
j=1
4 It should be noted that it is also necessary to pre-multiply the elements of Eq. (4) by L ′
and post-multiply them by L.

26 Alexis Lazaridis
where
⎛ ⎞
j∑
Q j = ⎝ A k − I⎠ .
k=1
3. The Singular Value Decomposition
Matrix in Eq. (5) may be augmented to accommodate, as an additional
column, the vector δ, µ or z. It is also possible to accommodate all these
vectors in the following way:
˜ = [ .δµz ] (6)
In this case, ˜ is defined on E n × E m , with m>n.
For conformability, the vector x i−p in Eq. (5) should be augmented
accordingly by using the linear advance operator L (such that L k y i = y i+k ),
i.e.,
⎡ ⎤
x i−p
1
˜x i−p = ⎢
⎣ L p ⎥
t i−p ⎦ .
L p d i−p
Hence, Eq. (5) takes the form:
p−1
∑
x i = Q j x i−j + ˜ ˜X i−p + w i . (7)
j=1
We can compute the unique generalized inverse (or pseudo-inverse) of ˜,
denoted by ˜ + (Lazaridis and Basu, 1981), from:
˜ + = VF ∗ U ′ (8)
where
V is of dimension (m×m), and its columns are the orthonormal eigenvectors
of ˜ ′ ˜.
U is (n × m), and its columns are the orthonormal eigenvectors of ˜ ˜ ′ ,
corresponding to the largest m eigenvalues of this matrix so that:
U ′ U = V ′ V = VV ′ = I m (9)
F is diagonal (m × m), with elements f ii f i , called the singular values
of ˜, which are the non-negative square roots of the eigenvalues of ˜ ′ ˜.

If the rank of ˜ is k, i.e.,
A Novel Method of Estimation Under Co-Integration 27
r( ˜) = k ≤ n, then f 1 ≥ f 2 ≥···≥f k > 0
and f k+1 = f k+2 =···=f m = 0
F ∗ is diagonal (m × m), and fii ∗ f i ∗ = 1/f i .
It should be noted that all the above matrices are real. Also note that if
˜ has full row rank, then ˜ + is the right inverse of ˜, i.e., ˜ ˜ + = I n
Hence, the singular value decomposition (SVD) of ˜ is:
˜ = UFV ′ . (10)
4. Computing the Co-Integrating Vectors
We proceed to form a matrix F 1 of dimension (m × n) such that:
f 1(i,j) =
{ 0, if i ̸= j
√
fi , if i = j
(11)
In accordance to Eq. (11), we next form a matrix F 2 of dimension (n × m).
It is verified that F 1 F 2 = F. Hence, Eq. (10) can be written as:
˜ = AC
where A = UF 1 of dimension (n×n) and C = F 2 V of dimension (n×m).
After normalization, we get the possible co-integrating vectors as the
rows of matrix C, whereas the elements of A can be viewed as approximations
to the corresponding coefficients of adjustment.
It is apparent that the co-integrating vectors can always be computed,
given that r( ˜) > 0. Needless to say that the same steps are followed if ,
instead of ˜, is considered.
5. Case Study 1: Comparing Co-Integrating Vectors
We first consider the VAR(2) model, presented by Holden and Peaman
(1994). The x ∼I(1) vector consists of the variables C (consumption), I
(income) and W (wealth), so that x ∈ E 3 . We used the same set of data
presented at the end of this book (Table D3, pp. 196–198). To simplify
the presentation, we did not consider the three dummies DD682, DD792,
and DD883. Hence, the VAR in this case has a form analogous to Eq. (1),
without trend and dummy components.

28 Alexis Lazaridis
Estimating the equations of this VAR by OLS, we get the following
results.
⎡
⎤ ⎡
⎤
0.059472 −0.073043 0.0072427
0.064873
⎢
⎥ ⎢
⎥
= ⎣0.5486237 −0.5244858 −0.028041 ⎦ , δ = ⎣ 0.16781451⎦ .
0.3595042 −0.2938160 −0.039400 −0.1554421
(12)
Hat (ˆ) is omitted for simplicity. One possible co-integration vector with
intercept, obtained by applying the ML method is:
1 − 0.9574698 − 0.048531 + 0.2912925 (13)
and corresponds to the long-run relationship:
C i = 0.9574698I i + 0.048531W i − 0.2912925.
For the vector in Eq. (13) to be a co-integration vector, the necessary and
sufficient condition is that the (disequilibrium) errors û i computed from:
û i = C i − 0.9574698I i − 0.048531W i + 0.2912925 (14)
to be stationary, i.e., {û i }∼I(0), since x ∼I(1).
For distinct purposes, these ML errors obtained from Eq. (14) will be
denoted by uml i .
Applying SVD on ˜ = [.δ] from Eq. (12), we get matrix C which is:
⎡
⎤
1 −0.9206225 −0.06545528 0.1110597
⎢
⎥
C = ⎣ 1 0.3586208 −0.6305243 −6.403011 ⎦
1 1.283901 −2.050713 0.4300255
⎛ ⎞
1.365344
⎜ ⎟
Euclidean norm = ⎝ 6.521098 ⎠ .
2.653064
In the column at the right-hand side, the (Euclidean) norm of each row
of C is presented. It is noted also that the singular values of are:
f 1 = 0.8979247, f 2 = 0.2304381 and f 3 = 0.0083471695.
All f i are less than 1, indicating thus that at least one row of C can be
regarded as a possible co-integration vector, in the sense that the resulting
errors are likely to be stationary. This row usually has the smallest norm,

A Novel Method of Estimation Under Co-Integration 29
which in this case, is the first one. Hence, the errors corresponding to this
co-integration vector are obtained from:
û i = C i − 0.9206225I i − 0.06545528W i + 0.1110597. (15)
These errors will be denoted by usvd i . It should be pointed out here
that the smallest norm condition is just an indication as to which row of
matrix C to be considered first.
It may be useful to re-call at this point that the co-integration vector
reported by the authors (p. 111), which is obtained by applying OLS after
omitting the first two observations from the initial sample is:
1 − 0.9109 − 0.0790 + 0.1778.
It should be clarified that this vector has been obtained by applying OLS
to estimate directly the long-run relationship. Repeating this procedure,
we get:
1 − 0.910971 − 0.079761 + 0.178455.
Hence, the errors are computed from:
û i = C i − 0.910971I i − 0.079761W i + 0.178455. (16)
These errors will be denoted by ubook i .
The next task is to compare the above three series of errors, having a
first look at the corresponding graphs, which are shown in Fig. 1.
Although by a first glance the three series seem to be stationary, we shall
go a bit further to see their properties in detail. Before going to the next
section, it is worth to mention here that for the three series, the normality
test using the Jarque-Bera criterion favors the null.
Figure 1. The series {uml i }, {usvd i }, and {ubook i }.

30 Alexis Lazaridis
5.1. Testing for Co-integration
Since for the first two cases, ∑ û i ̸= 0, we estimated the following regression:
q∑
û i = b 1 + b 2 û i−1 + b j+2 û i−j + ε i . (17)
The value of q was set such that the noises ε i to be white, as it will be
explained in detail later on. Regarding the last case, the intercept is omitted
from Eq. (17), since û i ’s are OLS residuals, so that ∑ û i = 0.
The estimation results are as follows:
u ˆml i =−0.00612 − 0.381773 uml i−1 − 0.281651uml i−1
(0.193688)
j=1
t =−3.682
uŝvd i = 0.006525 − 0.428278 usvd i−1 − 0.259066usvd i−1
(0.108269)
t =−3.956
ubôok i =−0.606759 ubook i−1
(0.09522)
t =−6.37.
Since these error series are the results of specific calculations and in
the simplest case are the OLS residuals, it is not advisable (Harris, 1995,
pp. 54–55). to apply the Dickey-Fuller (DF/ADF) test, as we do with any
variable in the initial data set. We have to compute the t u statistic from McKinnon
(1991, p. 267–276) critical values (see also Harris, 1995, Table A6,
p. 158). This statistic (t u = ∞ + 1 /T + 2 /T 2 ) for three (independent)
variables in the long-run relationship with intercept is:
α = 0.01 α = 0.05 α = 0.10
t u =−4.45 t u =−3.83 t u =−3.52.
Hence, {book i } is stationary for α = (0.01, 0.05, 0.10), {usvd i } is stationary
for α = (0.05, 0.10) and {uml i } is stationary only for α = 0.10.
Recall that the null [û i ∼ I(1)] is rejected in favor of H 1 [û i ∼ I(0)], if
t

A Novel Method of Estimation Under Co-Integration 31
It is obvious from these findings, the super consistency of the OLS.
However, the method we introduce here, produces almost minimum variance
errors, which is a quite desirable property, as suggested by Engle and
Granger (Dickey et al., 1994, p. 27). Hence, we will mainly focus on this
property in our next section.
6. Case Study 2: Further Evidence Regarding the Minimum
Variance Property
With the same set of data, the co-integration vector without an intercept
obtained by applying the ML method is:
1 − 0.9422994 − 0.058564
The errors corresponding to this vector are obtained from:
û i = C i − 0.9422994I i − 0.058564W i (18)
Again these errors will be denoted by uml i .
Next, we apply SVD to in Eq. (12) to obtain matrix C, which is:
⎡
⎤
1 −0.9192042 −0.066081211
⎢
⎥
C = ⎣ 1 1.160720 −1.012970 ⎦
1 0.9395341 2.063768
and
⎛ ⎞
1.359891
⎜ ⎟
Euclidean norm = ⎝ 1.836676 ⎠
2.47828
The singular values of are:
f 1 = 0.89514, f 2 = 0.0403121 and f 3 = 0.0026218249
Again, all f i ’s are less than 1. We consider the first row of C, so that
the errors corresponding to this vector are obtained from:
û i = C i − 0.9192042I i − 0.066081211W i (19)
These errors will be also denoted by usvd i .
The co-integrating vector reported by the authors (p. 109), which is
obtained from the VAR(2), including the dummies mentioned previously,

32 Alexis Lazaridis
by applying the ML procedure is given by:
1 − 0.93638 − 0.03804
and the errors obtained from this vector are computed from:
û i = C i − 0.93638I i − 0.03804W i (20)
As in the previous case, these errors will be denoted by ubook i .
The minimum variance property can be seen from the following:
Standard deviation of Standard deviation of Standard deviation of
{uml i } {usvd i } {book i }
0.0169 0.0166 0.0193
Next, we consider the model presented by Banerjee et al. (1993,
pp. 292–293) that refers to VAR(2) with constant dummy and trend. The
state vector x ∈ E 4 consists of the variables (m − p), p, y, and R. The
data (in logs) are presented in Harris (1995, statistical appendix, pp. 153–
155. Note that the entries for 1967:1 and 1973:2 have to be corrected from
0.076195 and 0.56569498 to 9.076195 and 9.56569498, respectively). Considering
the co-integration vector reported by the authors, which has been
obtained by applying the ML method, we compute the errors from:
û i = (m − p) i + 6.3966p i − 0.8938y i + 7.6838R i . (21)
These errors will be denoted by uml i .
Estimating the same VAR by OLS, we get,
⎡
⎤
−0.089584 0.16375 −0.184282 −0.933878
−0.012116 −0.9605 0.229635 0.206963
= ⎢
⎥
⎣ 0.021703 0.676612 −0.476152 0.447157 ⎦ ,
−0.006877 0.118891 0.048932 −0.076414
⎡ ⎤
⎡ ⎤
3.129631
0.001867
−2.46328
δ = ⎢ ⎥
⎣ 5.181506 ⎦ and µ =
−0.001442
⎢ ⎥
⎣ 0.003078 ⎦
−0.470803
−0.000366

A Novel Method of Estimation Under Co-Integration 33
Following the procedure described above, we obtain matrix C which is:
⎡
⎤
1 −48.30517 24.60144 37.75685
1 5.491415 −0.6510755 7.423318
C = ⎢
⎥
⎣ 1 −2.055229 −5.466846 0.9061699 ⎦
1 0.0051181894 0.1603713 −0.1244312
⎛ ⎞
66.06966
9.310488
Euclidean norm = ⎜ ⎟
⎝ 5.99429 ⎠
1.020406
The singular values of are:
f 1 = 1.503069, f 2 = 0.7752298, f 3 = 0.1977592
and f 4 = 0.012560162
The fact that one singular value is greater than one, is an indication that
unless a dummy is present — we hardly can trace one row of matrix C,
which may be related to stationary errors û i . As shown in Fig. 1, from the
graphs, from which refer to the errors corresponding to the rows of C, we
see that only the second row produces reasonably results. In this case, the
errors are computed from:
û i = (m − p) i + 5.491415p i − 0.6510755y i + 7.42318R i . (22)
As usual, these errors will be denoted by usvd i .
The minimum variance property can be seen from:
Standard deviation of {uml i } Standard deviation of {usvd i }
0.2671 0.2375
To see that none of the two error series is stationary, as it was indicated
by the first singular value, we present the following results.
u ˆml i = 0.268599 − 0.178771 uml i−1 − 0.214098uml i−1
(0.065634)
t =−2.724
uŝvd i = 0.832329 − 0.193432 usvd i−1 − 0.160135usvd i−1
(0.066421)
t =−2.912
For a long-run relationship with three (independent) variables without
trend and intercept, the critical value t u for α = 0.10 is less than −3.

34 Alexis Lazaridis
Nevertheless, the method proposed, produces better results than the ML
approach does.
Finally, we will consider the first of the two co-integration vectors
(since, it produces slightly better results), reported by Harris (1995, p. 102).
From this vector, which was obtained by the ML method, one gets the
following errors.
û i = (m − p) i + 7.325p i − 1.073y i + 6.808R i (23)
Also we obtain
standard deviation of û i ’s = 0.268 and
û i =−0.117378 − 0.178896
(0.068296) ûi−1 − 0.30095417û i−1
t =−2.619.
It is obvious that these additional results further support the previous
findings, which are due to some properties of SVD (Lazaridis, 1986).
6.1. A Note on Integration
It seems to be a common belief that differentiating a variable say n times,
we will always get a stationary series (Harris, 1995, p. 16). Hence, the
initial series is said to be I(n). But, this is not necessarily the case, as it is
verified that if we take into consideration the exports of goods and services
for Greece, as presented in Table 1. Besides if n is large enough, is it of
any good to obtain such a stationary series when economic variables are
considered?
Table 1. The series {x i }.
Exports of goods and services in bil. Eur. Greece 1956–2000.
X
2.4944974E-02 2.9053558E-02 2.9347029E-02 2.8760089E-02 2.8173149E-02
3.2575201E-02 3.5803374E-02 4.1379310E-02 4.2553190E-02 4.7248717E-02
6.6030815E-02 6.7498162E-02 6.6030815E-02 7.6008804E-02 8.8041089E-02
0.1000734 0.1300073 0.2022010 0.2664710 0.3325018
0.4258254 0.4763023 0.5998532 0.7325019 1.049743
1.239618 1.388114 1.788701 2.419956 2.868965
3.618782 4.510052 4.978430 5.818929 6.485106
7.690976 9.316215 9.847396 11.45708 14.08716
15.39428 18.87601 20.90506 22.56992 25.51577
Source: International Financial Statistics. (International Monetary Fund, Washington DC)

A Novel Method of Estimation Under Co-Integration 35
The series { ∆xi}, { ∆ 2 x i }, and { ∆
3 x i }
Figure 2. Differences of the NI series {x i }.
Using the series {x i } as shown in Table 1, we can easily verify from the
corresponding graph, that even for n = 5, the series { 5 x i } is not stationary.
In Fig. 2, the series {x i }, { 2 x i }, and { 3 x i } are presented, for a better
understanding of this situation. We will call the variables, which belong to
this category near the integrated (NI) (Banerjee et al., 1993, p. 95) series.
To trace that a given series is NI, we may run the regression:
x i = β 1 + β 2 x i−1 + β 3 t i +
q∑
β j+3 x i−j + u i (24)
which is a re-parametrized AR(q) with constant, where we added a trend
too. As shown in Eq. (17), the value of q is set such that the noises u i to
be white. A comparatively simple way for this verification is to compute
the residuals û i and to consider the corresponding Ljung-Box Q statistics
and particularly their p-values, which should be much greater than
0.1, to say that no autocorrelation (AC) is present. On the other hand, if
we trace heteroscedasticity, this is a strong indication that we have a NI
series. For the data presented in Table 1, we found that q = 2. The corresponding
Q statistics (Column 4) together with p-values are presented
in Table 2.
We see that for all k (column 1), the corresponding p-values (column 5)
are greater than 0.1. But, if we look at the residuals graph (Fig. 3), we can
verify the presence of heteroscedasticity.
j=1

36 Alexis Lazaridis
Table 2.
Residuals: Autocorrelations, PAC, Q statistics and p-values.
Autocorrelation (AC), partial autocor coefficients (PAC) Q statistics and p values (prob).
Values AC PAC Q Stat(L-B) p value Q Stat(B-P) p value
of k
1 0.040101 0.040101 0.072482 0.787756 0.067540 0.794952
2 −0.061329 −0.063039 0.246254 0.884151 0.225515 0.893367
3 −0.008189 −0.003064 0.249432 0.969240 0.228331 0.972891
4 −0.285494 −0.290504 4.213238 0.377916 3.651618 0.455202
5 0.042856 0.072784 4.304969 0.506394 3.728756 0.589090
6 0.099724 0.058378 4.815469 0.567689 4.146438 0.656867
7 −0.151904 −0.167680 6.033816 0.535806 5.115577 0.645861
8 −0.007846 −0.069642 6.037162 0.643069 5.118163 0.744875
9 0.001750 0.023203 6.037333 0.736176 5.118291 0.823877
10 0.109773 0.165620 6.733228 0.750367 5.624397 0.845771
11 0.134538 0.022368 7.812250 0.730017 6.384616 0.846509
12 −0.029101 −0.048363 7.864417 0.795634 6.420185 0.893438
13 −0.074997 −0.028063 8.222832 0.828786 6.656414 0.918979
14 −0.084284 −0.017969 8.691681 0.850280 6.954772 0.936441
15 −0.113984 −0.104484 9.580937 0.845240 7.500452 0.942248
16 −0.081662 −0.157803 10.05493 0.863744 7.780540 0.955133
17 −0.001015 −0.005026 10.05501 0.901288 7.780582 0.971016
18 −0.053178 −0.056574 10.27276 0.922639 7.899356 0.980097
Figure 3. The residuals from Eq. (24) (q = 2).

A Novel Method of Estimation Under Co-Integration 37
Another easy and practical way to trace heteroscedasticity, is to select
the explanatory variable, which yields the smallest p-value for the corresponding
Spearman’s correlation coefficient (r s ). Note that in models like
the one we have seen in Eq. (24), such a variable is the trend, resulting
in this case to: r s = 0.3739,t = 2.394,p = 0.0219. This means that
for a significance level α>0.022, heteroscedasticity is present. Hence,
we have an initially NI series {x i }, which has to be weighed somehow in
order to be transformed to a difference stationary series (DSS). In some
cases, this transformation can be achieved if the initial series is expressed
in real terms, or as percentage of growth. In usual applications, the (natural)
logs [i.e., ln(x i )] are considered, given that {x i /x i } > {ln(x i )} >
{x i /x i−1 }.
7. Case Study 3: How to Obtain Reliable Results Regarding
the Order of Integration?
It is a common practice to apply DF/ADF for determining the order of integration
for a given series. However, the analytical step-by-step application
of this test (Enders, 1995, p. 257; Holden and Perman, 1994, pp. 64–65),
leaves the impression that the cure is worse than the disease itself. On the
other hand, by simply adopting the results produced by some commercial
computer programs, which is the usual practice in many applications,
we may reach some faulty conclusions. It should be noted at this point that
according to the results obtained by a well-known commercial package, the
series {x i }, as shown in Table 1, should be considered as I(2), for α = 0.05,
which is not the case.
Here, we present a comparatively simple procedure to determine the
order of integration of a DSS, by inspecting a model analogous to Eq. (24).
Assuming that {z i } is DSS, we proceed as follows:
• Start with k = 1 and estimate the regression:
k z i = β 1 + β 2 k−1 z i−1 + β 3 t i +
q∑
β j+3 k z i−j + u i . (25)
Be sure that the noises in Eq. (25) are white, by applying the relevant
tests as described above. This way, we set the lag-length q. Note that if
k = 1, its value is omitted from Eq. (25) and that 0 z i−1 = z i−1 .
j=1

38 Alexis Lazaridis
Table 3.
Critical values for the DF F-test.
Sample size α = 0.01 α = 0.05 α = 0.10
25 10.61 7.24 5.91
50 9.31 6.73 5.61
100 8.73 6.49 5.47
250 8.43 6.34 5.39
500 8.34 6.30 5.36
>500 8.27 6.25 5.34
• Proceed to test the hypothesis:
H 0 : β 2 = β 3 = 0. (26)
To compare the computed F-statistic, we have to consider, in this case,
the Dickey-Fuller F-distribution. The critical values (Dickey and Fuller,
1981) are reproduced in Table 3, to facilitate the presentation.
Note that in order to reject Eq. (26), F-statistic should be much greater
than the corresponding critical values, as shown in Table 3. If we reject
Eq. (26), this means that the series {z i } is I(k − 1). If the null hypothesis
is not rejected, then increase k by 1(k = k + 1) and repeat the same
procedure, i.e., starting from estimating Eq. (25), testing at each stage so
that the model disturbances are white noises.
• In case of known structural break(s) in the series, a dummy d i should be
added in Eq. (25), such that:
{ 0 if i ≤ r
d i =
w i if i>r
where w i = 1(∀ i) for the shift in mean, or w i = t i for the shift in
trend. It is re-called that r denotes the date of the break or shift. With
this specification, the results obtained are alike the ones that Perron et al.
(1992a; b) procedure yields.
We applied the proposed technique to find the order of integration of the
variable m i as shown in Eq. (21), which is the log of nominal M1 (money
supply). Harris (1995, p. 38) after applying DF/ADF test reports that “...
and the interest rate as I(1) and prices as (I2). The nominal money supply
might be either, given its path over time....”. Since the latter variable is m i ,
it is clear that, with this particular test, it was not possible to get a precise
answer as to whether {m i } is either I(1) or I(2).

A Novel Method of Estimation Under Co-Integration 39
To show the details, underline the first stage of this procedure; we
present some estimation results with different values of q.
For q = 3
Most of the p-values in the 5th column of the table, which is analogous
to Table 2, are equal to zero.
Obviously, this is not the proper lag-length.
For q = 4
All p-values are greater than 0.1, as shown in Table 2. r s =−0.193,
p = 0.05652. F(2, 94) = 4.2524.
This lag-length is acceptable.
For q = 5
All p-values are greater than 0.1, as shown in Table 2. r s =
−0.2094,p= 0.0395.F(2, 92) = 4.2278.
This lag-length is questionable, since for α>0.04, we face the problem
of heteroscedasticity.
q = 6
All p-values are greater than 0.1, as we have seen in Table 2. r s =
−0.166,p= 0.1038.F(2, 90) = 5.937.
This lag-length is quite acceptable.
q = 7
All p-values are greater than 0.1, as shown in Table 2. r s =−0.1928,p=
0.0608.F(2, 88) = 4.768.
This lag-length is also acceptable, but it is inferior when compared to
the previous one.
From these analytical results, it can be easily verified that the proper
lag-length is 6 (q = 6). It may also be worthy to mention that according
to the normality test (Jarque-Bera), we should accept the null. The value
of F = 5.937 is less than the corresponding critical values as shown in
Table 3, for 100 observations and α = (0.01, 0.05). Hence, we accept
Eq. (26) and increase the value of k by one. The estimation results, after
properly selecting the value of q(q = 5), are:
2 m i = 0.0047 − 0.894892 m i−1 + 0.00033 t i
(0.0046) (0.21784) (0.000108)
+
5∑
ˆβ j+3 2 m i−j +û i . (27)
j=1
Regarding the residuals, all p-values in the 5th column of the table,
which is analogous to Table 2, are greater than 0.1. Further, we have:
r s =−0.1556,p= 0.127. Jarque-Bera = 0.8(p = 0.67).F(2, 91) = 8.44.

40 Alexis Lazaridis
Figure 4. The series {m i } and { 2 m i }.
Since F

A Novel Method of Estimation Under Co-Integration 41
Due to the properties of SVD, we can easily and directly include in the
co-integrating vectors, as many deterministic components as we want to.
Besides, we found that the errors corresponding to the finally selected cointegration
vector, are characterized by the minimum variance property. It
should be noted that the procedure proposed here is not mentioned in the
relevant literature.
Further, we analyzed the stages of a relevant technique to obtain reliable
results regarding the order of integration of a given series provided that
it is DSS. We also demonstrated the properties of the so-called near integrated
series, which can be traced by applying this technique. It should be
emphasized that with this kind of series (NI), we show that the conventional
methods for unit root test may produce faulty results.
References
Banerjee, A, JJ Dolado, JW Galbraith and DF Hendry (1993). Co-integration, Error Correction,
and the Econometric Analysis of Non-Stationary Data. New York: Oxford
University Press.
Dickey, DA and WA Fuller (1981). Likelihood ratio statistics for autoregressive time series
with a unit root. Econometrica 49, 1057–1072.
Dickey, DA, DW Jansen and DL Thornton (1994). A primer on cointegration with an application
to money and income. In Cointegration for the Applied Economist, BB Rao
(ed.), UK: St. Martin’s Press, 9–45.
Enders, W (1995). Applied Econometrics Time Series. New York: John Wiley.
Harris, R (1995). Using Cointegration Analysis in Econometric Modelling. London: Prentice
Hall.
Holden, D and R Perman (1994). Unit roots and cointegration for the economist. In Cointegration
for the Applied Economist, BB Rao (ed.), UK: St. Martin’s Press, 47–112.
Johansen, S and K Juselius (1990). Maximum likelihood estimation and inference on cointegration
with application to the demand for money. Oxford Bulletin of Economics and
Statistics 52, 169–210.
Johnston, J and J DiNardo (1997). Econometric Models. New York: McGraw-Hill International.
Kleibergen, F and V Dijk (1994). Direct cointegration testing in error correction models.
Journal of Econometrics 63, 61–103.
Lazaridis, A and D Basu (1983). Stochastic optimal control by pseudo-inverse. Review of
Economics and Statistics 65(2), 347–350.
Lazaridis, A (1986). A note regarding the problem of perfect multicollinearity. Quantity and
Quality 120, 297–306.
McKinnon, J (1991). Critical values for co-integration tests. In Long-Run Economic Relationships,
RF Engle and CWJ Granger (eds.), New York: Oxford University Press.
Perron, P and T Vogelsang (1992a). Nonstationarity and level shifts with an application
to purchasing power parity. Journal of Business and Economic Statistics 10,
301–320.

42 Alexis Lazaridis
Perron, P and T Vogelsang (1992b). Testing for a unit root in a time series with a changing
mean: Corrections and extensions. Journal of Business and Economic Statistics 10,
467–470.
Sims, CA (1980). Macroeconomics and reality. Econometrica 48, 1–48.

Topic 2
Time Varying Responses of Output to Monetary
and Fiscal Policy
Dipak R. Basu
Nagasaki University, Nagasaki, Japan
Alexis Lazaridis
Aristotle University of Thessalonikki, Greece
1. Introduction
There are large volumes of literatures on the effectiveness of monetary and
fiscal policies and on lags in the effects of monetary policies (Friedman and
Schwartz, 1963; Hamburger, 1971; Meyer, 1967; Tobin, 1970). Although
the lengths of lags are important in determining the role of monetary-fiscal
policies, the relationship between money and income vary over time due
to changes in the lag structure. Mayer (1967), Poole (1975) and Warburton
(l971) attempted to analyze the empirical variability of the lag structure
by analyzing the turning points in general business activity. Sargent and
Wallace (1973) as well as Lucas (1972) have drawn attention to the role of
time-dependant response coefficients to changes in stabilization policies.
Cargill and Meyer (1977; 1978) have estimated the time-varying relationship
between national income and monetary-fiscal policies. The results
then indicated existences of time variations and exclusions of time variations
of the coefficients, lead to exclusions of prior information inherent in
the models from the estimation process. Blanchard and Perotti (2002) as
well as Smets and Wouters (2003) have obtained similar characteristics of
the monetary and fiscal policy.
The existence of time dependency of effects of monetary fiscal policies,
reflects considerable doubts on the policy prescription based on constant
coefficient estimates. However, more reasonable results can be obtained if
we try to estimate dynamics and movements of these relationships over
43

44 Dipak R. Basu and Alexis Lazaridis
time. For this purpose, adaptive control systems with time-varying parameters
(Astrom and Wittenmark, 1995; Basu and Lazaridis, 1986; Brannas
and Westlund, 1980; Nicolao, 1992; Radenkovic and Michel, 1992) provide
a fruitful approach. There are alternative estimation methods, e.g., rational
expectation modeling, VAR approaches etc., to estimate time-varying systems.
These methods, however, are mainly descriptive, i.e., cannot have
immediate application in policy planning. The purpose of this paper is to
explore this possibility in terms of a planning model where adaptive control
rules will be implemented so that we can derive time-varying reduced form
coefficients from the original structural model to demonstrate the dynamics
of monetary-fiscal policies.
The model follows the basic theoretical ideas of monetary approach to
balance of payments and structural adjustments (Berdell, 1995; Humphrey,
1981; 1993; Khan and Montiel, 1989). In Section 2, the method of adaptive
optimization and the updating method of the time-varying model are analyzed.
In Section 3, the model and its estimates are described. This includes
some necessary adjustments for a developing country. In Section 4, the
results of the time-varying impacts of monetary-fiscal policies are analyzed.
2. The Method of Adaptive Optimization
Suppose a dynamic econometric model can be converted to an equivalent
first order dynamic system of the form
˜x i = Øx i−1 + ˜Cũ i + ˜D˜z i +ẽ i (1)
where ˜x i is the vector of endogenous variables, ũ i is the vector of control
variables, ˜z i is the vector of exogenous variables, and ẽ i is the vector
of noises, which are assumed to be white Gaussian and Ã, ˜C, and ˜D are
coefficient matrices of proper dimensions. It should be noted that a certain
element of ˜z i is 1 and corresponds to the constant terms. The parameters of
the above system are assumed to be random.
Shifting to period i + 1, we can write
˜x i+1 = Øx i + ˜Cũ i+1 + ˜D˜z i+1 +ẽ i+1 . (2)
Now, we define the following augmented vectors and matrices.
[ ] [ ] [ ]
˜xi
˜xi+1
ẽi+1
x i = , x
ũ i+1 = , e
i ũ i+1 = ,
i+1 0
A =
[ ]
à 0
, C =
0 0
[ ] ˜C
, D =
I
[ ] ˜D
.
0

Time Varying Responses 45
Hence (2) can be written as
x i+1 = Ax i + Cũ i+1 + D˜z i+1 + e i+1 (3)
Using the linear advance operator L, such that L k y i = y i+k and defining
the vectors u, z and ε from
then Eq. (3) can take the form
u i = Lũ i
z i = L˜z i
ε i = Le i
x i+1 = Ax i + Cu i + Dz i + ε i (4)
which is a typical linear control system.
We can formulate an optimal control problem of the general form
T −1
min J = 1 2 ‖x T −ˆx T ‖ 2 Q T
+ 1 ∑
‖x i −ˆx i ‖ 2 Q
2
i
(5)
subject to the system transition equation shown in Eq. (4).
It is noted that T indicates the terminal time of the control period, {Q}
is the sequence of weighing matrices and ˆx i (i = 1, 2,...,T)is the desired
state and control trajectory, according to our formulation.
The solution to this problem can be obtained according to the minimization
principle by solving the Ricatti-type equations (Astrom and
Wittenmark, 1995).
K T = Q T (6)
i =−(E i C ′ K i+1 C) −1 (E i C ′ K i+1 A) (7)
K i = E i A ′ K i+1 A + ′ i (E iC ′ K i−1 A) + Q i (8)
h T =−Q T ˆx T (9)
h i = i (E i C ′ K i+1 D)z i + i (E i C ′ )h i+1
+ (E i A ′ K i+1 D)z i + (E i A ′ )h i+1 − Q i ˆx i (10)
g i =−(E i C ′ K i+1 C) −1 [(E i C ′ K i+1 D)z i + (E i C ′ )h i+1 ] (11)
xi ∗ = [E i A + (E i C) i ] xi ∗ + (E iC) g i + (E i D)z i (12)
u ∗ i = i xi ∗ + g i (13)
i=1

46 Dipak R. Basu and Alexis Lazaridis
where u ∗ i (i = 0, 1,...,T − 1), the optimal control sequence and x∗ i+1 , the
corresponding state trajectory, which constitutes the solution to the stated
optimal control problem.
In the above equations, i is the matrix of feedback coefficients and
g i is the vector of intercepts. The notation E i denotes the conditional
expectations, given all information up to the period i. Expressions like
E i C ′ K i+1 C, E i C ′ K i+1 A, E i C ′ K i+1 D are evaluated, taking into account
the reduced form coefficients of the econometric model and their covariance
matrix, which are to be updated continuously, along with the implementation
of the control rules. These rules should be re-adjusted according
to “passive-learning” methods, where the joint densities of matrices A, C,
and D are assumed to remain constant over the control period.
2.1. Updating Method of Reduced-Form Coefficients and Their
Co-Variance Matrices
Suppose we have a simultaneous-equation system of the form
XB ′ + UƔ ′ = R (14)
where X is the matrix of endogenous variable defined on E N × E n and
B is the matrix of structural coefficients, which refer to the endogenous
variables and is defined on E n ×E n . U is the matrix of explanatory variables
defined on E N ×E g and Ɣ is the matrix of the structural coefficients, which
refer to the explanatory variables, defined on E N × E g . R is the matrix of
noises defined on E N ×E n . The reduced form coefficients matrix is then
defined from:
=−B −1 Ɣ.
(14a)
Goldberger et al. (1961) have shown that the asymptotic co-variance
matrix, say of the vector ˆπ, which consists of the g column of matrix ˆ
can be approximated by
˜ =
[[ ˆ
I g
]
⊗ ( ˆB ′ ) −1 ] ′
F
[[ ˆ
I g
]
⊗ ( ˆB ′ ) −1 ]
(15)
where ⊗ denotes the Kroneker product, ˆ and ˆB are the estimated coefficients
by standard econometric techniques and F denotes the asymptotic
co-variance matrix of the n + g columns of ( ˆB ˆƔ), which assumed to be
consistent and asymptotically unbiased estimate of (BƔ).

Time Varying Responses 47
Combining Eqs. (14) and (14a) we have
BX ′ =−ƔU ′ + R ′ ⇒ X ′ =−B −1 ƔU ′ + B −1 R ′
⇒ X ′ = U ′ + W ′ (16)
where W ′ = B −1 R ′
Denoting the ith column of matrix X ′ by x i and the ith column of matrix
W ′ by w i , we can write
⎡
⎤
u 1i 0 ··· 0 u 2i 0 ··· 0 u gi 0 ··· 0
0 u 1i ··· 0 0 u 2i ··· 0 0 u gi ··· 0
x i =
· · · · · · · · ·
⎢ · · · · · · · · ·
⎥
⎣ · · · · · · · · · ⎦
0 0 ··· u 1i 0 0 ··· u 2i ··· 0 ... u gi
π + w i
(17)
where u ij is the element of the jth column and ith row of matrix U. The
vector π ∈ E ng , as mentioned earlier, consists of the g column of matrix .
Equation (17) can be written in a compact form, as
x i = H i π + w i , i = 1, 2,...,N (17a)
where x i ∈ E n ,w i ∈ E n and the observation matrix H i is defined on
E n × E ng .
In a time-invariant econometric model, the coefficients vector π is
assumed random with constant expectation overtime, so that
π i+1 = π i , for all i. (18)
In a time-varying and stochastic model we can have
π i+1 = π i + ε i
(18a)
where ε i ∈ E ng is the noise.
Based on these, we can re-write Eq. (17a) as
x i+1 = H i+1 π i+1 + w i+1 i = 0, 1,...,N − 1. (19)
We make the following assumptions.
(a) The vector x i+1 and matrix H i+1 can he measured exactly for all i.
(b) The noises ε i and w i+1 are independent discrete white noises with
known statistics, i.e.,
E(ε i ) = 0; E(w i+1 ) = 0
E(ε i w ′ i+1 ) = 0

48 Dipak R. Basu and Alexis Lazaridis
E(c i ε ′ i ) = Q 1δ ij ,
E(w i w ′ i ) = Q 2δ ij .
where δ ij is the Kronecker delta, and
The above co-variance matrices, assumed to be positive definite.
(c) The state vector is normally distributed with a finite co-variance matrix.
(d) Regarding Eqs. (18a) and (19), the Jacobians of the transformation of
ε i into π i+1 and of w i+1 into x i+1 are unities. Hence, the corresponding
conditional probability densities are:
p(π i+1 |π i ) = p(ε i )
p(x i+1 |π i+1 ) = p(w i+1 ).
Under the above assumptions and given Eqs. (18a) and (19), the problem
set is to evaluate
and
E(π i+1 |x i+1 ) = π ∗ i+1
cov (π i+1 |x i+1 ) = S i+1
(the error co-variance matrix)
where x i+1 = x 1 ,x 2 ,x 3 ,...,x i+1 .
The solution to this problem (Basu and Lazaridis, 1986; Lazaridis,
1980) is given by the following set of recursive equations, as it is briefly
shown in Appendix A.
π ∗ i+1 = π∗ i + K i+1(x i+1 − H i+1 π ∗ i ) (20)
K i+1 = S i+1 H i+1 ′ Q−1 2
(21)
Si+1 −1 i+1 + H i+1 ′ Q−1 2 H i+1 (22)
Pi+1 −1 1 + S i ) −1 . (23)
The recursive process is initiated by regarding K 0 and H 0 as null matrices
and computing π ∗ 0 and S 0 from
π0 ∗ =ˆπ i.e., the reduced form coefficients (columns of matrix ˆ)
S 0 = P 0 = ˜.
The reduced form coefficients, along with their co-variance matrices,
can be updated by this recursive process and at each stage the set of Riccati

Time Varying Responses 49
equations should be updated accordingly so that adaptive control rules may
be derived.
Once we estimate the model (described in the next section), using the
full information maximum likelihood (FIML) method, we can obtain both
the structural model and the probability density functions along with all
associated matrices mentioned above. We first convert the structural econometric
model to a state-variable form according to Eq. (1). Once we specify
the targets for the state and control variables, the objective function is to be
minimized, the weights attached to each state and control variables, then
we can calculate the results of the optimization process for the entire period
using Eqs. (6)–(13). Thereafter, we can update all probability density functions
and all other associated matrices using Eqs. (20)–(23). These will
effectively update the coefficients of the model in its state-variable form.
We can repeat the optimization process over and over as we update the
model, its associated matrices, probability density functions and use these
as new information. When the process will converge, i.e., the difference
between the old and new estimates are insignificant according to some preassigned
criteria, we can obtain the final updated coefficients of the model
along with the results of the optimization process. The dynamics of the
time-varying coefficients (in terms of response-multipliers) are described
later in Section 4. This mechanism is a great improvement compared to the
fixed-coefficient model as we can incorporate in our calculation, changing
information sets derived from the implementation of the optimization
process.
3. Monetary-Fiscal Policy Model
We describe below a monetary-fiscal policy model, which was estimated
with data from the Indian economy. The model accepts the definition of
balance of payments and money stock according to monetary approach
of balance of payments (Khan, 1976; Khan and Montiel, 1989; 1990).
The decision to choose this particular model is influenced by the fact that
it is commonly known as the fund-bank adjustment policy model, used
extensively by the World Bank and the International Monetary Fund (IMF).
In the version adopted for this paper, there is no explicit investment
or consumption function, because the domestic absorption can reflect the
combined response of both private and public investment and consumption,
to the planned target for national income set by the planning authority
and to various market forces reflected in the money market interest

50 Dipak R. Basu and Alexis Lazaridis
rate and exchange rate. The “New Cambridge” model of the UK economy
(Cripps and Godley, 1976; Godley and Lavoie, 2002; 2007) has postulated
a similar combined consumption-investment function for the UK
as well.
The model was estimated by applying FIML method, using the data
from the Indian economy for the period 1951–1996. The estimated parameters
were then used as the initial starting point for the stochastic control
model. The estimated econometric model can be transformed into a state
variable form (Basu and Lazaridis, 1986), in order to formulate the optimal
control problem, i.e., to minimize the quadratic objective function, subject
to Eq. (4), which is the system transition equation. As already mentioned,
the recursive estimation process of the time-varying response-multipliers
is presented in brief in Appendix A.
3.1. Absorption Function and National Income
Domestic absorption reflects the behavior of both the private and public
sector regarding consumption and investment too. Domestic real adsorption
is influenced by real national income, market interest rate and foreign
exchange rate. We assume a linear relationship.
(A/P) t = a 0 + a 1 (Y/P) t − a 2 (IR) t − a 3 EXR t ,
t = time period.
The relation between the national income and adsorption can be defined
as follows:
Y t = A t + TY t + R t − G t + GBS t − LR t
where A is the value of domestic absorption, P is the price level, Y is the
national income, IR is the market interest rates, EXR is the exchange rate,
TY is the government tax revenue, G is the public consumption, GBS is the
government bond sales, LR is the net lending by the central government to
the states (which is not part of the planned public expenditure) and R is
the changes in the foreign exchange reserve reflecting the behavior of the
foreign trade sector.
The government budget deficit (BD t ) is defined by the following
equation
BD t = (G t + LR t + PF t ) − (TY t + GBS t + AF t + BF t )
where PF is the foreign payments due to existing foreign debts, which
may include both amortization and interest payments, AF is the foreign

Time Varying Responses 51
assistance which is an insignificant feature, FB is the total foreign borrowing,
assuming only the government can borrow from foreign sources.
We assume AF and LR as exogenous, whereas FB, G, and TY as policy
instruments. However, PF depends on the level of existing foreign debt and
the world interest rate, although a sizable part of the foreign borrowing can
be at a concessional rate
PF t = a 4 + a 5
t∑
r=−20
( ) WIR
FB r + a 6 .
EXR t
Government bond sales (GBS) depends on its attractiveness reflected on
the interest rate (IR), on the ability of the domestic economy to absorb (A)
on the requirements of the government (G) and on the alternative sources of
finances reflected on the tax revenue (TY) and on government’s borrowing
from the central bank i.e., the net domestic asset (NDA) creation by the
central bank.
GBS t = a 7 + a 8 A t + a 9 IR t + a 10 G t − a 11 TY t − a 12 NDA t
3.2. Monetary Sector
We assume the flow equilibrium in the money market, i.e.,
MD t = M t = MS t
where MD is the money demand and MS is the money supply. The stock
of money supply depends on the stock of high powered money and the
money-multiplier, as follows:
MS t = [(1 + CD)/(CD + RR)] t (R + NDA) t .
(R + NDA) reflect the stock of high-powered money and the expression
within the square bracket is the money-multiplier, which depends on credit
to deposit ratio of the commercial banking sector (CD) and the reserve to
deposit liabilities in the commercial banking sector (RR). Whereas NDA
is an instrument, R depends on the foreign trade sector. However, the
government can influence CD and RR to control the money supply. RR,
which is the actual reserve ratio, depends on the demand for loans created by
private sectors and the commercial bank’s willingness to lend. We assume
that the desired reserve ratio RR ∗ t is a function of national income and

52 Dipak R. Basu and Alexis Lazaridis
market interest rate i.e.,
RR ∗ t = a 13 + a 14 Y t + a 15 IR ∗ t .
The commercial banks may adjust their actual reserve ratio to the
desired reserve ratio with a lag.
Thus, we can write
RR t = α(RR ∗ t − RR t−1 )
where 0

Time Varying Responses 53
The import cost in turn depends on the exchange rate (EXR) and the world
price of imported goods (WPM). We assume the desired price level (P ∗ )is
represented by the following equation:
P ∗ t = a 27 − a 28 (A t ) + a 29 (IMC t ).
The desired price level reflects private sector’s reaction to their expected
domestic absorption of the expected import cost. Suppose the actual price
will move according to the difference between the desired price in period t
and the actual price level in the previous period
Pt = β(P ∗ t − P t−1 );
0

54 Dipak R. Basu and Alexis Lazaridis
3.5. Stability of the Model
Characteristic roots (real) of the system transition matrix
− 0.0000008
− 0.0000008
− 0.1213610
0.2442519
0.3087129
0.5123629
0.7824260
0.0000001
0.0000001
All the roots are real and they are less than unity, so the system is
stable. [In the equivalent control system, the rank of the controllability
matrix is the same as the dimension of the reduced state vector so that the
system is controllable and observable, i.e., the system parameters can be
identified.]
We can, however, transform our model to the following form:
Y t = ρY t−1 + e t , t = 1, 2,...,n (24)
where ρ is a real number and (e t ) is a sequence of normally distributed
random variables with mean zero and variance σt 2 . Box and Pierce (1970)
suggested the following test statistic
where
Q m = n
m∑
rk 2 (25)
k=1
/(
n∑
n∑
r k = ê t ê t−k
t=k+1 t=1
ê 2 t
)
(26)
n = the number of observations, m = n − k, where k = the number of
parameters estimated, and ê t are the residuals from the fitted model.
If (Y t ) satisfies the system, then under the null hypothesis, Q m is
distributed as a chi-squared random variable with m degrees of freedom.
The null hypothesis is that ρ = 1 where ê t = Y t − Y t−1 and thus k = 0.

Time Varying Responses 55
The estimated value of Q m is 3.85, where the null hypothesis is rejected
at 0.05 significance level. So, we accept the alternative hypothesis that if
ρ

56 Dipak R. Basu and Alexis Lazaridis
Table 4. Response-multiplier period 3.
Endogenous Y GBS P BD CD MS IR
EXR −0.02199 −0.00069 0.05269 0.00133 −0.00042 −0.00573 −0.00062
G 0.03001 0.00499 0.16536 0.02924 0.05923 0.04217 0.00570
TY −0.02470 −0.01149 −0.16281 0.02472 −0.07031 −0.06325 −0.02220
CI 0.00215 0.04676 −0.00252 −0.00399 −0.00465 −0.00671 0.06228
Table 5. Response-multiplier period 5.
Endogenous Y GBS P BD CD MS IR
EXR −0.02133 −0.00088 0.05190 0.00152 −0.00201 −0.00595 −0.00089
G 0.02058 0.00558 0.18078 0.01160 0.50890 0.07248 0.00530
TY −0.01676 −0.00410 −0.16655 0.00695 −0.55026 −0.07779 −0.01013
CI 0.00268 0.04465 −0.00267 −0.00403 −0.01967 −0.00726 0.05953
Table 6. Response-multiplier period 7.
Endogenous Y GBS P BD CD MS IR
EXR −0.02067 −0.00116 0.04987 0.00135 −0.00104 −0.00558 −0.00129
G 0.00733 0.01033 0.16455 0.00048 0.57357 0.10760 0.01206
TY −0.00402 −0.00345 −0.14832 −0.01434 −0.58067 −0.10904 −0.00869
CI 0.00200 0.04174 −0.00236 −0.00293 −0.02186 −0.00551 0.05566
Table 7.
Response of output to monetary and fiscal policies.
Periods 1 2 3 5 7
dY/dCI −0.00226 −0.00273 −0.00215 −0.00268 −0.00200
dY/dEXR −0.02254 −0.02209 −0.02188 −0.02133 −0.02067
dP/dG 0.14849 0.15603 0.16536 0.18078 0.16455
dY/dG 0.03572 0.03203 0.03001 0.02058 0.00733
dP/dTY −0.15549 −0.15688 −0.16281 −0.16655 −0.14832
dY/dTY −0.03590 −0.02691 −0.02470 −0.01676 −0.00402
dGBS/dG 0.00403 0.00568 0.00499 0.00558 0.01033

Time Varying Responses 57
4. Policy Analysis
The dynamics of the monetary and fiscal policy are analyzed in terms of
the analysis of the dynamic response-multipliers and their relationship with
the monetary-fiscal policy regimes. The response-multiplier of the system
will move over time within an adaptive control framework (Tables 1–6).
The movements of the coefficients response of response-multipliers in a
monetary policy framework are described below. It is essential that for the
stability of the control system, these dynamics of the response-multiplier
should be slow (Das and Cristi, 1990; Tsakalis and Ioannou, 1990).
Analysis of the response-multipliers shows that devaluation would have
negative effect on the national income, devaluation would also have negative
effect on the government bond sales, CD, interest rate, and money
demand. This is due to the fact that Indian exports may not be that elastic
in response to devaluation, whereas devaluation will reduce import abilities
significantly. As a result, national income and domestic activity would
have negative effects, which would depress the activity of the private sector.
Because of this CD will decline.
Due to the downturn of the economic activity, there will be less demand
for government bonds. Devaluations also can have an inflationary effect due
to increased import costs. Government expenditure, on the other hand, will
have positive effects on every variable. This implies that increased public
expenditure will stimulate the national income and the private sector despite
increased interest rate. However, the increased public expenditure will have
inflationary impacts on the economy at the same time.
Increased tax revenue will depress national income, as it will reduce
government bond sales. Lower level of national income will reduce money
supply and the private sector’s activity, which will be reflected in the reduced
currency to deposit ratio and the reduced level of money demand. Reduced
level of national income, in this case, will have reduced price level but budget
deficit will go up as well because of the reduced demand for government
bonds. Increased rate of central bank’s discount rate will depress national
income and general price level. At the same time, private sector’s activity
will be reduced, as reflected in the CD and money demand, due to increased
rate of interest. Although government bond sales will go up, budget deficit
will be increased due to reduced level of economic activity.
The effect of the central bank discount rate (CI ) on interest rate varies
from 0.061 in period 1 to 0.055 in period 7. This result is primarily due to
the fact that the influence of G (public expenditure) on IR has increased
from 0.003 in period 1 to 0.012 in period 7. If the public expenditure goes

58 Dipak R. Basu and Alexis Lazaridis
up, there will be direct pressure on the central bank to provide loans to the
government. The central bank can put pressure on the commercial banks to
extend some loans in public sector and less to the private sector, and the CD
of the commercial banks will be reduced as a result (at the same time reserve
ratio will be increased). While CD goes up in response to government
expenditure (G), the CI will have a similar effect on the currency to deposit
ratio.
Effects of the CD on prices declines rapidly, whereas the effect of the
exchange rate on price level is most prominent and does not vary much. It
demonstrates that although during the initial phase of planning, tight credit
policy may influence prices, in the longer run structural factors, public
expenditure, and import costs reflected through the exchange rate will affect
price levels more significantly. The effect of the CI on the money supply
(MS) will be reduced from −0.005 in period 1 to −0.007 in period 6, and
it will slightly increase in period 7.
The impacts of the public expenditure and tax revenues on the two most
important variables, GNP (Y) and price level (P) can be analyzed as follows.
The increased government expenditure (G) will increase price level and
the impact will be intensified. The impact of the government expenditure
on the GNP will be reduced, which is consistent with the reduced impacts
of the tax revenues on the GNP over the planning period. Tax revenue will
have negative impacts on the GNP as well as on the price level, and the
impacts will decline over time. The negative impacts of the tax revenue on
the GNP is partly explained by the negative effects of tax revenue on the
currency to deposit ratios of the commercial banks, the main indicator for
the private sector activities. The government expenditure also have positive
impacts on the government bond sales and the impact will increase over
time due to the increasing difficulties of raising taxes, which will have
negative impacts on the growth prospects.
The effect of the exchange rate declines gradually, whereas the effect of
the interest rate is cyclical. This is due to the cyclical pattern of the central
discount rate in the optimum path. It is quite obvious that the impacts of
fiscal and monetary policies on output will fluctuate over time depending
on the direction of change of these policies. The variations of the effects are
not unsystematic, as feared by Friedman and Schwartz (1963). However,
here we are analyzing an optimum path not the historical path.
5. Conclusion
The importance of time-varying coefficients was recognized in statistical
literature long ago (Davis, 1941), where frequency domain approach of

Time Varying Responses 59
the time series analysis was utilized (Mayer, 1972). Several authors since
then have used varying parameter regression analysis (Cooley and Prescott,
1973; Farley et al., 1975). In the above analysis, adaptive control system
was used in a state-space model where the reduced form parameters can
move over time.
However, variations over time are slow which indicates any absence
of explosive response (Das and Cristi, 1990; Tsakalis and Ioannou, 1990).
Cargil and Mayer (1978) also have observed stable movements of the coefficients.
Thus the role of the monetary-fiscal policies on the economy is not
unsystematic, although it can vary over time.
Results obtained by other researchers showed that the effects of
monetary and fiscal policy change over time, and it is important to analyze
these changes in order to obtain time-consistent monetary-fiscal policy (De
Castro, 2006; Folster and Henrekson, 2001; Muscatelli and Tirelli, 2005).
The results obtained by using adaptive control method, showed similar
characteristics of the monetary-fiscal policy.
The implication for the public policy is quite obvious. Time-consistent
monetary-fiscal policy demands continuous revision, otherwise, the effectiveness
of the policy may deteriorate and as a result, the effects of monetary
and fiscal policy on major target variables of the economy may deviate from
their desired level. Our approach is a systematic way forward to analyze
these dynamics of monetary and fiscal policy.
References
Astrom, KJ and K Wittenmark (1995). Adaptive Control. Reading, MA: Addison-Wesley.
Basu, D andA Lazaridis (1986).A method of stochastic optimal control by Bayesian filtering
techniques. International Journal of System Sciences 17(1), 81–85.
Brannas, K and A Westlund (1980). On the recursive estimation of stochastic and time
varying parameters in economic system. In Optimization Techniques, K Iracki (ed.),
Berlin: Springer Verlag, 265–274.
Berdell, JF (1995). The prevent relevance of Hume’s open-economy monetary dynamics.
Economic Journal l05(432), September, 1205–1217.
Box, GEP and DA Pierce (1970). Distribution of residual autocorrelation in autoregressiveintegrated
moving average time series models. Journal of the American Statistical
Association 65(3), 1509–1526.
Blanchard, O and R Perotti (2002). An empirical characterization of the dynamic effects of
changes in government spending and taxes on output. Quarterly Journal of Economics,
117(4), November, 1329–1368.
Cargil, TF and RA Meyer (1977). Intertemporal stability of the relationship between interest
races and prices. Journal of Finance 32, September, 427–448.
Cargil, TF and RA Mayer (1978). The time varying response of income to changes in
monetary and fiscal policy. Review of Economics and Statistics LX(1), February, 1–7.

60 Dipak R. Basu and Alexis Lazaridis
Cripps, F and WAH Godley (1976). A formal analysis of the Cambridge economic policy
group Model. Economica 43, August, 335–348.
Cooley, TF and EC Prescott (1973). An adaptive regression model. International Economic
Review l4, June, 248–256.
Das, M and R Cristi (1990). Robustness of an adaptive pole placement algorithm
in the presence of bounded disturbances and slow time variation of parameters.
IEEE Transactions on Automatic Control 35(6), June, 762–802.
Davis, HT (1941). The Analysis of Economic Time Series. Bloomington: Principia Press.
De Castro, F (2006). Macroeconomic effects of fiscal policy in Spain. Applied Economics
38(8–10), May, 913–924.
Farley, J, M Hinich and T McGuire (1975). Some comparison of tests for a shift in the slopes
of a multivariate time series model. Journal of Econometrics 3, August, 297–318.
Friedman, M and A Schwartz (1963). A monetary history of the United States, 1867–1960.
Princeton: Princeton University Press.
Folster, S and M Henrekson (2001). Growth effects of government expenditure and taxation
in rich countries. European Economic Review 45(8), 1501–1520.
Goldberger, AC, AL Nagar and HS Odeh (1961). The covariance matrices of reduced
form coefficients and forecasts for a structural econometric model. Econometrica 29,
556–573.
Godley, W and M Lavoie (2002). Kaleckian models of growth in a coherent stock-flow
monetary framework: A Kaldorian view. Journal of Post Keynesian Economics 24(2),
277–312.
Godley, W and M Lavoie (2007). Fiscal policy in a stock-flow consistent (SFC) model.
Journal of Post Keynesian Economics 30(1), 79–100.
Hamberger, MJ (1971). The lag in the effect of monetary policy:A survey of recent literature.
Monthly Review-Federal Reserve Bank of New York, December, 289–297.
Humphrey, TM (1981). Adam Smith and the monetary approach to the balance of payments.
Economic Review, Federal Reserve Bank of Richmond 67.
Humphrey, TM (1993). Money, Ranking and Inflation. Aldershot: Edward Elgar.
Khan, MS (1976).A monetary model of balance of payments: The case ofVenezuela. Journal
of Monetary Economics 2, July, 311–332.
Khan, MS and PJ Montiel (1989). Growth oriented adjustment programs. IMF Staff Papers
36, June, 279–306.
Khan, MS and PJ Montiel (1990), A marriage between fund and bank models. IMF Staff
Papers 37, March, 187–191.
Lazaridis, A (1980). Application of filtering methods in econometrics. International Journal
of Systems Science 11(11), 1315–1325.
Lucas, RE, Jr (1972). Expectation and the neutrality of money. Journal of Economic Theory
4, April, 103–124.
Meyer, T (1967). The lag in effect of monetary policy, some criticisms. Western Economic
Journal 5, September.
Mayer, R (1972) Estimating coefficients that change over time. International Economic
Review 11, October.
Muscatelli, VA and P Tirelli (2005). Analyzing the interaction of monetary and fiscal policy:
does fiscal policy play a valuable role in stabilization. CESIFO Economic Studies 51(4),
1–17.
Nicolao, G (1992). On the time-varying Riccati difference equation of optimal filtering.
SIAM Journal on Control and Optimization 30(6), November, 1251–1269.

Time Varying Responses 61
Poole, W (1975). The relationship of monetary deceleration to business cycle peaks. Journal
of Finance 30, June, 697–712.
Radenkovic, M and A Michel (1992). Verification of the self-stabilization mechanism in
robust stochastic adaptive control using Lyapunov function arguments. SIAM Journal
on Control and Optimization 30(6), November, 1270–1294.
Sargent, TJ and N Wallace (1973). Rational expectations and the theory of economic policy.
Journal of Monetary Economics 2, April, 169–183.
Smets, V and R Wouters (2003). An estimated dynamic stochastic general equilibrium
model of the Euro area. Journal of European Economic Association 1(5), September,
1123–1175.
Tobin, J (1970). Money and income: Post Hoc Ergo Propter Hoc. Quarterly Journal of
Economics 84, May, 301–317.
Tsakalis, K and P Ioannou (1990). A new direct adaptive control scheme for time-varying
plant. IEEE Transactions on Automatic Control 35(6) June, 356–369.
Warburton, C (1971). Variability of the lag in the effect of monetary policy 1919–1965.
Western Economic Journal 9, June, 1919–1965.
Appendix A
Probability Density Function and Recursive Process
for Re-Estimation
Under the assumptions stated in Section 3 and according to Bayes’ rule, the
conditional probability density function of π i given x i+1 is Gaussian and is
given by:
∫
p(π i+1 |x i+1 ) = p(π i |x i )p(π i+1 ,x i+1 |π i ,x i )dπ i
where
(
p(π i+1 |x i ) = constant exp − 1 )
2 ||π i+1 − πi ∗ ||2 Si
−1
πi ∗ = E(π i |x i )
S i = cov(π i |x i )
(S i assumed to be invertible)
[
P(π i+1 ,x i+1 |π i ,x i ) = constant exp − 1 ∥ π i+1 − π i ∥∥∥
2
2 ∥ x i+1 − H i+1 π i+1
C =
[ ] [
Q1 0
, C
0 Q −1 Q
−1
=
2
1
0
0 Q −1
2
]
.
C −1 ]

62 Dipak R. Basu and Alexis Lazaridis
Hence
∫
p(π i+1 |x i+1 ) = constant
(
exp − 1 )
J
2 ˜ i dπ i
where
J˜
i = (π i − πi ∗ )′ (Si
−1 + Q −1
1 )(π i − πi ∗ )
+ (π i+1 − πi ∗ )′ (Q −1
1
+ H i+1 ′ Q−1 2 H i+1)(π i+1 − πi ∗ )
− 2(π i − πi ∗ )′ Q −1
1 (π i − πi ∗ )
+ (x i+1 − H i+1 πi ∗ )′ Q −1
2 (x i+1 − H i+1 πi ∗ )
− 2(π i+1 − πi ∗ )′ H i+1 ′ Q−1 2 (x i+1 − H i+1 πi ∗ ). (a)
Now, define G −1
i
= (S −1
i
+ Q −1
1
) and consider the expression
J˜
i = [(π i − πi ∗ )′ − G i Q −1
1 (π i+1 − πi ∗ )]′
× G −1
i
[(π i − πi ∗ )′ − G i Q −1
1 (π i+1 − πi ∗ )]. (b)
Note that G i is symmetric, since it is the sum of two (symmetric) co-variance
matrices. Expanding Eq. (b) and noting that G i G −1
i
= I we obtain
J˜
i = (π i − πi ∗ )′ G −1
i
(π i+1 − πi ∗ ) − 2(π i − πi ∗ )′ Q −1
1 (π i+1 − πi ∗ )
+ (π i+1 − πi ∗ )′ Q −1
1 G iQ −1
1 (π i+1 − πi ∗ ). (c)
In view of Eqs. (b) and (c), Eq. (a) can be written as
J˜
i = [(π i − πi ∗ )′ − G i Q −1
1 (π i+1 − πi ∗ )]′
× G −1
i
[(π i − πi ∗ )′ − G i Q −1
1 (π i+1 − πi ∗ )]
+ (π i+1 − πi ∗ )′ (Q −1
1
+ H i+1 ′ Q−1 2 H i+1 − Q −1
1 G iQ −1
1 )(π i+1 − πi ∗ )
+ (x i+1 − H i+1 πi ∗ )′ Q −1
2 (x i+1 − H i+1 πi ∗ )
− 2(π i+1 − πi ∗ )′ H i+1 ′ Q−1 2 (x i+1 − H i+1 πi ∗ ).
∫ ( )
Integration with respect to π i yields constant exp −
1 ˜ 2
J i dπi =
constant exp ( − 1 ...
3 J i)
where
...
J i = ( π i+1 − πi ∗ )′ (Q −1
1
− Q −1
1 G iQ −1
1
+ H i+1 ′ Q−1 2 H i+1) ( π i+1 − πi
∗ )
+ ( x i+1 − H i+1 πi ∗ )′ Q −1 (
2 xi+1 − H i+1 πi
∗ )
− 2 ( π i+1 − πi ∗ )′ H i+1 ′ ( Q−1 2 xi+1 − H i+1 πi
∗ )
.

Time Varying Responses 63
Hence
(
p(π i+1 |x i+1 ) = constant exp − 1 )
...
J i .
2
Since p(π i+1 |x i+1 ) is proportional to the likelihood function, by maximizing
the conditional density function, we are also maximizing the likelihood
in order to determine πi+1 ∗ ...
. Note that minimization of J i, is equivalent to
maximizing p(π i+1 |x i+1 ). To minimize ...
J i, we expand Eq. (c) eliminating
terms not containing π i+1 . Then, we differentiate with respect to π
i+1 ′ and
after equating to zero, we finally obtain (Lazaridis, 1980).
πi+1 ∗ = π∗ i + (Q−1 1
− Q −1
1 G iQ −1
1
+ H i+1 ′ Q−1 2 H i+1) −1
× H i+1 ′ Q−1 2 (x i+1 − H i+1 πi ∗ ). (d)
Now, consider the composite matrix:
Q −1
1
− Q −1
1 G iQ1 −1 where G i = (Si
−1 + Q −1
1 )−1 .
Considering the matrix identity of householder, we can write
Q −1
1
− Q −1
1 (S−1 i
+ Q −1
1 )−1 Q −1
1
= (Q 1 + S i ) −1 Pi+1 −1 .
Hence Eq. (d) takes the form:
πi+1 ∗ = π∗ i + K i+1(x i+1 − H i+1 πi ∗ )
where K i+1 ,Si+1 −1 and P−1
i+1
are defined in Eqs. (21)–(23).
It is recalled that H 0 is a null matrix, since no observations exist beyond
period 1 in the estimation process. The same applies for the vector x 0 .
Appendix B
It is recalled that the model was estimated using FIML method. The FIML
estimates are as follows (R 2 and adjusted R 2 refer to the corresponding 2
SLS estimates. Numbers in brackets are the corresponding t-statistics).
Estimated Model
1. A t = 0.842Y t
(3.48)
+ 55191.5
(4.87)
+ 0.024A t−1 − 1.319IR t + 1.051IR t−t − 284EXR t
(1.74) (1.34) (1.16) (1.29)
R 2 = 0.99, R 2 = 0.92, DW = 1.76, ρ = 0.27

64 Dipak R. Basu and Alexis Lazaridis
2. (Y t ) = A t + R t
3. (BD) t = (G t + LR t + PF t ) − (TY t + GBS t + AF t + FB t )
4. PF t = 1148.80 + 0.169 CFB t−1 + 144.374 WIR t
(1.48) (2.39)
(1.89)
5. GBS t = 0.641G t
(1.14)
+ 0.677G t−1
(1.41)
+ 1.591IR t
(1.64)
− 0.33AF t
(0.23)
R 2 = 0.89, R 2 = 0.84, DW = 2.36, ρ = 0.23
(1.51)
6. MD = MS
7. (MS) t = [(1 + CD t )/(CD t + RR t )](R t + NDA t )
8. RR t = 0.008Y t
(3.47)
+ 0.065
(2.72)
9. CD t = 0.4391IR t
(−1.49)
10. MD t = 2.733RR t
(−2.52)
− 0.002Y t−1
(−1.84)
+ 1.2571R t
(1.87)
+ 2.7031R t−1
(1.88)
− 0.003T
(2.87)
R 2 = 0.86, R 2 = 0.79, DW = 2.88, ρ = 0.26
(1.23)
− 0.0057T
(−6.269) + 0.193
(11.95)
+ 0.158CD t−1 + 0.0007Y t + 0.009Y t−1
(1.16) (1.56) (1.73)
R 2 = 0.94, R 2 = 0.92, DW = 1.22, ρ = 0.64
(4.21)
− 2.19IR t
(−0.24)
+ 1.713IR t−1 + 1.275Y t
(2.17) (6.67)
− 113335.0
(−0.088)
R 2 = 0.86, R 2 = 0.81, DW = 1.92, ρ = 0.26
(1.31)
11. IR t = 0.413MD t−1
(1.93)
+ 0.406Y t−1
(1.56)
12. P t = 0.0004A t
(−5.71)
− 0.814IR t−1 + 8.656CI t − 1.351CI t−1
(1.403) (1.68)
− 7.02
(−1.84)
R 2 = 0.98, R 2 = 0.95, DW = 2.48,ρ = 0.58
(3.21)
+ 0.0002A t−1 + 0.105IMC t
(1.77)
(1.48)
+ 0.421P t−1
(3.79)
R 2 = 0.98, R 2 = 0.93, DW = 2.09,ρ = 0.48
13. IMC t = 5.347 + 19.352WPM t + 9.017EXR t
(1.34) (2.03)
(0.97)
R 2 = 0.98, R 2 = 0.97, DW = 2.07, ρ = 0.31
(1.37)
14. R t = X t − IM t + K t + PFT t + FB t − PF t + AF t
+ 32.895
(1.87)

15. IM t =−24.04 − 0.025IM t−1
(−0.82)
+ 1.123T
(0.27)
16. CFB t = ∑ t
r=−20 FB r
(−0.86)
+ 0.104Y t
(1.59)
Time Varying Responses 65
− 0.089Y t−1 − 0.654IMC t
(9.21) (−1.26)
R 2 = 0.96, R2 = 0.92, DW = 2.52, ρ =−0.62
(−1.72)
λ 2 = 563.09
The estimated Chi-square satisfies the goodness of fit test for the FIML
estimation.
Notations
A = Domestic absorption
AF = Foreign receipts (grants etc.)
BD = Government budget deficits
CD = Credit to deposit ratio in the commercial banking sector
CFB = Cumulative foreign borrowing, i.e., foreign debt over a period of
20 years
CT = Discount rate of the RBI
FB = Foreign borrowing
G = Government expenditure
GBS = Government bond sales
IM = Value of imports
IMC = Import price index (1990 = 100)
IR = Interest rate in the money-market
K = Foreign capital inflows
LR = Lending (minus repayments to the states)
MD = Money demand
MS = Money supply
NDA = Net domestic asset creation by the RBI
P = Consumers’ price index (1990 = 100)
PFT = Private foreign transactions
PF = Foreign payments
R = Changes in foreign exchange reserve
RR = Reserve to deposit ratio in the commercial banking sector
TY = Government tax revenue
T = Time trend

66 Dipak R. Basu and Alexis Lazaridis
WPM = World price index of India’s imports (1990 = 100)
WIR = World interest rate, average of European and US money market
rate
EXR = Exchange rate (Rs/US$)
X = Value of exports
Y = GNP at constant 1990 prices

Chapter 3
Mathematical
Modeling in Macroeconomics

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Topic 1
The Advantages of Fiscal Leadership in an
Economy with Independent Monetary Policies
Andrew Hughes Hallet
James Mason University, USA
1. Introduction
In January 2006, Gordon Brown (as Britain’s finance minister) was widely
criticized by the European Commission and other policy makers for running
fiscal policies, which they considered to be too loose and irresponsible. The
UK fiscal deficit had breached the 3% of GDP that is considered to be safe.
To make its point, the European Commission initiated an “excessive deficit”
procedure against the UK government, claiming that its fiscal policies constituted
a danger for the good performance of the UK economy and its
neighbors, if these deficits were not contained and reversed. Yet the United
Kingdom, alone among its European partners, allows fiscal policy to lead in
order to achieve certain social expenditure and medium-term output objectives
and a degree of co-ordination with the monetary policies designed to
reach a certain inflation target. And the economic performance has been
no worse, and may have been better than elsewhere in the Eurozone. Was
Gordon Brown’s strategy so mistaken after all?
The British fiscal policy has changed radically since the days when it
tried to micro-manage all of the aggregate demand with an accommodating
monetary policy in the 1960s and 1970s; and again during the 1980s, it
was designed to strengthen the economy’s supply-side responses, while the
monetary policies were intended to secure lower inflation.
The 1990s saw a return to more activist fiscal policies — but policies
designed strictly in combination with an equally active monetary policy
based on inflation targeting and an independent Bank of England. They are
set, in the main, to gain a series of medium- to long-term objectives — low
debt, the provision of public services and investment, social equality, and
economic efficiency. The income stabilizing aspects of the fiscal policy
69

70 Andrew Hughes Hallet
have, therefore, been left to act passively through the automatic stabilizers,
which are part of any fiscal system, while the discretionary part (the bulk of
the policy measures) is set to achieve these long-term objectives. Monetary
policy, meanwhile, is left to take care of any short-run stabilization around
the cycle; that is, beyond what, predictably, would be done by the automatic
stabilizers. 1
To draw a sharp distinction between actively managed long-run policies,
and non-discretionary short-run stabilization efforts restricted to the
automatic stabilizers, is of course the strategic policy prescription of Taylor
(2000). Marrying this with an activist, monetary policy directed at cyclical
stabilization, but based on an independent Bank of England and a monetary
policy committee with the instrument (but not target) independence,
appears to have been the innovation in the UK policies. It implies a leadership
role for the fiscal policy, which allows both fiscal and monetary
policies to be better co-ordinated — but without either losing their ability
to act independently. 2
Thus, Britain appears to have adopted a Stackelberg solution, which lies
somewhere between the discretionary (but Pareto superior) co-operative
solution, and the inferior but independent (non-co-operative) solution, as
shown in Fig. 1. 3 Nonetheless, by forcing the focus onto long-run objectives,
to the exclusion of the short term, this set-up has imposed a degree of
pre-commitment (and potential for electoral punishment) on fiscal policy
because governments naturally wish to lead. But, the regime remains nonco-operative
so that there is no incentive to renege on earlier plans in the
1 The Treasury estimates that the automatic stabilizers will, in normal circumstances, stabilize
some 30% of the cycle; the remaining 70% being left to monetary policy (HM Treasury,
2003). The option to undertake discretionary stabilizing interventions is retained “for
exceptional circumstances” however. Nevertheless, the need for any such additional interventions
is unlikely: first, because of the effectiveness of the forward looking, symmetric
and an activist inflation targeting mechanism adopted by the Bank of England; and, second,
because the long-term expenditure (and tax) plans are deliberately constructed in nominal
terms so that they add to the stabilizing power of the automatic stabilizers in more serious
booms or slumps.
2 For details on how this leadership vs. stabilization assignment is intended to work, see HM
Treasury (2003) and Section 3 below. Australia and Sweden operate rather similar regimes.
3 Figure 1 is the standard representation of the outcomes of the different game theory equilibria
when the reaction functions form an acute angle. The latter is assured for our context
when both sets of policy makers have some interest in inflation control and output stabilization,
and the policy multipliers have the conventional signs (Hughes Hallett and Viegi,
2002). Stackelberg solutions, therefore, imply a degree of co-ordination in the outcomes,
relative to the non-co-operative (unco-ordinated) Nash solution.

The Advantages of Fiscal Leadership in an Economy 71
Figure 1.
Monetary-Fiscal Interactions and the Central Bank.
absence of changes in information. Thus, the policies and their intended
outcomes will be sustained by the government of the day. 4
2. The Fiscal Leadership Hypothesis
The hypothesis is that the United Kingdom’s improved performance is due
to the fact that the fiscal policy leads an independent monetary policy. This
leadership derives from the fact that fiscal policies typically have long-run
targets (sustainability and low debt), and is not easily reversible (public services
and social equality), and does not stabilize well if efficiency is to be
maintained. Nevertheless, there are also automatic stabilizers in any fiscal
policy framework, implying that monetary policy must condition itself on
the fiscal stance at each point. This automatically puts the latter in a follower’s
role. This is helpful because it allows the economy to secure the benefits
of an independent monetary policy but also enjoys a certain measure
of co-ordination between the two sets of policy makers — discretionary/
automatic fiscal policies on one side, and active monetary policies on the
4 Stackelberg games, with fiscal policy leading, produce fiscal commitment: i.e., sub-game
perfection with either strong or weak time consistency (Basar, 1989). In this sense, we have
“rules rather than discretion”. Commitment to the stabilization policies is then assured by
the independence of the monetary authority.

72 Andrew Hughes Hallet
other. The extra co-ordination arises in this case because the constraints
on, and responses to an agreed leadership role reduce the externalties of
self-interested behavior, which independent agents would otherwise impose
on one another. This allows a Pareto improvement over the conventional
non-co-operative (full independence) solution, without reducing the central
bank’s ability to act independently. It is important to realize that the
co-ordination here is implicit and therefore rule-based, not discretionary.
To show that the UK fiscal policy does lead monetary policy in this
sense, and that this is the reason for the Pareto improved results in Table 1,
I produce evidence in three parts:
• Institutional evidence: taken from the UK Treasury’s own account of
how its decision-making works, what goals it needs to achieve, and how
the monetary stance may affect it or vice versa;
Table 1.
Generalized Taylor rules in the UK and EU-12.
S.No. Const r t−1
π j,k
e
j, k gap pd debt
Dependent variable: central bank lending rate, r t :
For the UK, monthly data from June 1997–January 2004
(1) −1.72 0.711 1.394 +6, +18 0.540
(2.16) (5.88) (2.66)
(2.06)
(2) −2.57
(2.59)
0.598
(4.38)
R 2 = 0.91, F 3,21 = 82.47, N = 29
1.289
(0.66)
+9, +21 1.10
(1.53)
— —
−0.67
(0.83)
0.43
(0.50)
R 2 = 0.90, F 5,19 = 44.1, N = 25
For the Eurozone (EU-12), monthly data from January 1999–January 2004
(1) −0.996
(0.76)
(2) −13.67
(0.59)
0.274
(1.04)
0.274
(1.04)
1.714
(3.89)
+9, +21 0.610
(1.77)
R 2 = 0.82, F 3,11 = 22.2, N = 15
1.110
(1.19)
−6, +6 0.341
(1.22)
— —
0.463
(2.89)
R 2 = 0.87, F 5,13 = 24.7, N = 19
0.191
(0.63)
Notation: j, k give the bank’s inflation forecast interval; πj,k e represents the average inflation
rate expected over the interval t + j to t + k: Eπ t+j,t+k ;gap= GDP–trend GDP; pd =
primary deficit/surplus as a percentage of GDP (a surplus > 0) and debt = debt/GDP ratio.
Estimation: instrumented 2SLS; t-ratios in parentheses; j, k determined by search; and the
output gap is obtained from a conventional HP filter to determine trend output.

The Advantages of Fiscal Leadership in an Economy 73
• Empirical evidence: the extent to which the monetary policy is affected
by the fiscal policy, but fiscal policy with its longer objectives does not
depend on monetary policies and
• Theoretical evidence: shows how, with different goals for governments
and central banks, Pareto improving results can be expected from fiscal
leadership. The United Kingdom has, therefore, had the incentive, and
the capacity, to operate in this way.
3. Institutional Evidence: The Treasury’s Mandate
3.1. History
The British fiscal policy has changed a great deal over the past 30 years.
Fiscal policy was the principal instrument of the economic policy in the
1960s and 1970s, and was focused almost exclusively on demand management.
Monetary policy and the provision of public services (subject to a
lower bound) were essentially accommodating factors, since the main constraint
was perceived to be the financing of persistent current-account trade
deficits. The result of this was a short-term view, in which the conflicts
between the desire for growth (employment) and the recurring evidence
of overheating (trade deficits) led to an unavoidable sequence of “stop-go”
policies. There were many (Dow, 1964), who argued that the real problem
was a lack of long-run goals for the fiscal policy; and that the lags inherent
in recognizing the need for a policy change and in implementing it through
Parliament till it takes hold in the markets, had produced a system that was
actually destabilizing rather than stabilizing. But, there would have been
conflicts anyway because there were two or more competing goals, but
effectively only one instrument to reach them.
Such a system could not provide the long-run goal of public services,
public investment, and social equity. It certainly proved too difficult to turn
the fiscal policy on and off as fast and frequently as required, and precommit
to certain expenditure and taxation plans at the same time. The
point here is that, if you cannot pre-commit fiscal policy to certain goals,
then you will not be able to pre-commit monetary policy either. This means
that the “stable growth with low inflation” objective will be lost.
In the 1980s, the strategy changed when a new regime took office, committed
to reducing the size and role of the government in the economy. The
demand management role of the fiscal policy was phased out. This role
passed over to inflation control and monetary management — with limited

74 Andrew Hughes Hallet
success in the earlier phases of monetary and exchange rate targeting, but
with rather more success when it was formalized as an inflation-targeting
regime under an independent Bank of England and monetary policy committee.
In this period, therefore, the role of fiscal policy was to provide
the “conditioning information” within which the monetary management
had to work. It was split into two distinct parts. Short-term stabilization
of output and employment was left to the automatic stabilizers inherent in
the prevailing tax and expenditures rules. Discretionary adjustments would
only be used in exceptional circumstances, if at all. 5 The rest of the fiscal
policy, being the larger part, could then be directed at long-term objectives:
in this instance, changes to free up the supply side (and enhance competitiveness)
on the premise that greater microeconomic flexibility would
both reduce the need for stabilizing interventions (relative wage and price
adjustments would do the job better) and provide the conditions for stronger
employment and growth (HMT, 2003). Given this, the long-run goals of
better public services, efficiency, and social equity could then be attained.
In addition, as the market flexibility changes were made, this part of fiscal
policy could be increasingly focused on providing the long-run goals
directly. 6
3.2. Current Practice
According to the treasury’s own assessment (HMT, 2003), the UK fiscal policy
now leads monetary policy in two senses. First, fiscal policy is decided
in advance of monetary or other policies (pp. 5, 63, 64, 74), 7 and with a
long-time horizon (pp. 5, 42, 48, 61). Second, monetary policy is charged
with controlling inflation and stabilizing output around the cycle — rather
than steering the economy as such (pp. 61–63). Fiscal policy, therefore, sets
the conditions within which monetary policy has to respond and achieve its
own objectives (pp. 9, 15, 67–68). The short-term fiscal interventions, now
less than half the total and declining (p. 48, Box 5.3, Section 6), are restricted
to the automatic stabilizers — with effects that are known and predictable.
5 This follows the recommendations in Taylor (2000). However, because of the inevitable
trade-off between cyclical stability and budget stability, it is likely to be successful only in
markets with sufficiently flexible wages and prices (see Fatas et al., 2003).
6 This summary is taken from the UK Treasury’s own view (HMT, 2003), Sections 2, 4, and
pp. 34–38.
7 In this section, page or section numbers given without further reference are all cited from
HMT (2003).

The Advantages of Fiscal Leadership in an Economy 75
The short-run discretionary components are negligible (p. 59, Table 5.5),
and the long-run objectives of the policy will always take precedence in
cases of conflict (pp. 61, 63–68). Fiscal policy would, therefore, not be
used for fine tuning (pp. 11, 63), or for stabilization (pp. 1, 14). This burden
will be carried by interest rates, given the fiscal stance and its forward plans
(pp. 1, 7, 11, 37).
Third, given the evidence that consumers and firms often do not look
forward efficiently and may be credit-constrained, and also that the impacts
of the fiscal policy are uncertain and have variable lags (pp. 19, 26, 48;
Taylor, 2000), it makes sense for the fiscal policy to be used consistently
and sparingly and in a way that is clearly identified with the long-term
objectives. The United Kingdom has determined these objectives to be (pp.
11–13, 39–41, 61–63, 81–82):
(a) The achievement of sustainable public finances in the long term; low
debt (40% of GDP) and symmetric stabilization over the cycle.
(b) A sustainable and improving delivery of public services (health and education);
improving competitiveness/supply-side efficiency in the long
term; and the preservation of social (and inter-generational) equity and
alleviation of poverty.
(c) Recognition that the achievement of these objectives is often contractual
and cannot easily be reversed once committed. The long lead times
needed to build up these programs mean that the necessary commitments
must be made well in advance. Frequent changes would conflict
with the government’s medium-term sustainability objectives, and cannot
be fulfilled. Similarly, changes in direct taxes will affect both equity
and efficiency, and should seldom be made.
(d) The formulation of clear numerical objectives is consistent with these
goals; a transparent set of institutional rules to achieve them; and a commitment
to a clear separation of these goals from economic stabilization
around the cycle. 8
(e) To ensure that fiscal policy can operate along these lines, public expenditures
are planned with fixed three-year departmental expenditure limits
which, when combined with decision and implementation lags of up
to two years, means that the bulk of the fiscal policy has to be planned
8 The credibility of fiscal policy, and by extension an independent monetary policy, is seen as
depending on these steps, and on symmetric stabilization. See also Dixit (2001), and Dixit
and Lambertini (2003).

76 Andrew Hughes Hallet
with a horizon of up to five years — vs a maximum of two years in
the inflation targeting rules operated by the Bank of England. Moreover,
these spending limits are constraints defined in nominal terms, so
that they will be met. In addition, the Treasury operates a tax smoothing
approach — having rejected “formulaic rules” that might have
adjusted taxes or expenditures, or the various tax regulators, or credit
taxes that could have stabilized the economy in the short term. The
bulk of fiscal policy will remain focused on the medium to long term
therefore.
To summarize, the institutional structure itself has introduced fiscal
leadership. And, since the discretionary elements are smaller than elsewhere
— smaller than the automatic stabilizers (Tables 1–5) and declining
(Box 5.3) — something else (monetary policy) must have taken up the burden
of short-run stabilization. This arrangement is, therefore, best modeled
as a Stackelberg game, with institutional parameters for goals, independence,
priorities etc. I shall argue that this has had the very desirable result
of increasing the degree of co-ordination between policy makers without
compromising their formal or institutional independence — or indeed, their
credibility for delivering stability and low inflation. Constrained independence,
in other words, designed to reduce the externalities, which each party
might, otherwise, impose on the other.
4. Empirical Evidence
The next step is to establish whether the UK authorities have followed
the leadership model described above. The fact that they say that they
follow such a strategy does not prove that they do so. The difficulty
here is that, although the asymmetry in ex-ante (anticipated) responses
between the follower and leader is clear enough in the theoretical model —
the follower expects no further changes from the leader after the follower
chooses his reaction function, whereas the leader takes this reaction
function into account — such an asymmetry and zero restriction
will not appear in the ex-post (observed) responses that emerge in the
final solution (Basar and Olsder, 1999; Brandsma and Hughes Hallett,
1984; Hughes Hallett, 1984). Since I have no data on anticipations, this
makes it difficult to test for leadership directly. But, we can use indirect
tests based on the degree of competition, or complimentarity, between the
instruments.

4.1. Monetary Responses
The Advantages of Fiscal Leadership in an Economy 77
For monetary policy, it is widely argued that the authorities’ decisions can
best be modeled by a Taylor rule 9 :
r t = ρr t−1 + αE t π t+k + βgap t+h α, β, ρ ≥ 0 (1)
where k, h represent the authorities’forecast horizon 10 and may be positive
or negative. Normally, α>1 will be required to avoid indeterminancy:
that is, arbitrary variations in output or inflation, as a result of unanchored
expectations in the private sector. The relative size of α and β then reveals
the strength of the authorities’ attempts to control inflation vs. income stabilization;
and ρ their preference for gradualism. I set h = 0 in Eq. (1),
since monetary policy appears not to depend on the expected output gaps
(Dieppe et al., 2004).
In order to obtain an idea of the influence of fiscal policies on monetary
policy, I include some Taylor rule estimates — with and without fiscal
variables — in Table 1. They show such rules for the United Kingdom and
the Eurozone since 1997 and 1999, respectively, the dates when new policy
regimes were introduced. The Eurozone has been included to emphasize
the potential contrast between fiscal leadership in the United Kingdom, and
the lack of it in Europe.
4.2. Different Types of Leadership
Conventional wisdom would suggest that Europe has either monetary leadership
or independent policies, and hence policies which are either jointly
dependent in the usual way, or which are complementary and mutually supporting.
The latter implies that the monetary policy tends to expand/contract
whenever fiscal policy needs to expand or contract — but not necessarily
vice versa, when money is expanding or contracting and is sufficient to
9 Taylor (1993b). One can argue that the policy should be based on fully optimal rules
(Svensson, 2003), of which Eq. (1) will be a special case. But, it is hard to argue that policy
makers actually do optimize when the additional gains from doing so may be small and when
the uncertainties in their information, policy transmissions, or the economy’s responses may
be quite large. In practice, therefore, the Taylor rule approach is often found to fit central
bank behavior better.
10 In principle, k and h may be positive or negative: positive if the policy rule is based on
future-expected inflation, to head off an anticipated problem, as in the Bank of England. But
negative if interest rates are to follow a feedback rule to correct past mistakes or failures.

78 Andrew Hughes Hallet
control inflation on its own. This is a weak form of monetary leadership in
which fiscal policies are an additional instrument for use in cases of particular
difficulty, rather than the policies in a Nash game with conflicting
aims that need to be reconciled.
More generally, leadership implies complimentarity among policy
instruments in the leader’s reaction function, but conflicts among them in
the follower’s responses. A weak form of leadership also allows for independence
among instruments in the leader’s policy rules. Thus, monetary
leadership would imply some complimentarity (or independence) in the
Taylor rule, but conflicts in the fiscal responses.And fiscal leadership would
mean complimentarity or independence in the fiscal rule, but conflicts in
the monetary responses. Evidently, from Section 3, we might expect Stackelberg
leadership (with fiscal policy leading) in the UK, but the opposite in
the Eurozone.
4.3. Observed Behavior
The upper equations in each panel of Table 1 yield the standard results for
the monetary behavior in both the United Kingdom and the Eurozone. Both
monetary authorities have targeted expected inflation more than the output
gap since the late 1990s — and with horizons of 18–21 months ahead. The
European Central Bank (ECB) has been more aggressive in this respect.
But, contrary to conventional wisdom, it was also more sensitive to the
output gap and had a longer horizon and less policy inertia.
However, if we allow monetary policies to react to the changes in fiscal
stance, we get different results (the lower equations). Here, we see that the
UK monetary decisions may take fiscal policy into account, but the effect is
not significant or well defined. However, this model of monetary behavior
does imply more activist policies, a longer forecast horizon (up to two years
as the Bank of England claims) and greater attention to the output gap —
the symmetry in the UK’s policy rule. And to the extent that fiscal policy
does have an influence, it would be as a substitute (or competitor) for monetary
policy — fiscal deficits lead to higher interest rates. This is potentially
consistent with fiscal leadership, since this form of leadership can allow
independence or complimentarity between instruments in the leader’s rule.
We need to check the fiscal reaction functions directly. The lack of significance
for the debt ratio is easily understood, however. Since this is a
declared long-run objective of the fiscal policy, it would not be necessary
for the monetary policy to take it into account. So far, the evidence could

The Advantages of Fiscal Leadership in an Economy 79
imply a Stackelberg follower role or independence for monetary policy,
easing the competition (externalities) among policy instruments.
The ECB results look quite different. Once fiscal effects are included,
the concentration on inflation control is much reduced and the forecast
horizon shrinks to six months. Moreover, a feedback element, to correct
the past mistakes, comes in. At the same time, output stabilization becomes
less important, which implies that the symmetric targeting goes out. Instead,
monetary policy now appears to react to fiscal policy, but with the “wrong”
sign: the larger the primary deficit, the looser will be the monetary policy.
In this case, therefore, the policies are acting as complements — circumstances,
which call for a primary deficit will also call for a relaxation of the
monetary policy. Thus, we have an evidence of monetary leadership, where
fiscal policy is used as an additional policy instrument.
4.4. Fiscal Reaction Functions in the UK and Eurozone
Many analysts have hypothesized that fiscal policy responses can best be
modeled by means of a “fiscal Taylor rule”:
d t = a t + γgap t + sd γ > 0 (2)
where sd = structural deficit ratio, d t is the actual deficit ratio (d >0
denotes a surplus), 11 and a t represents all the other factors such as the
influence of monetary policy, existing or anticipated inflation, the debt burden,
or discretionary fiscal interventions. The coefficient γ then gives a
measure of an economy’s automatic stabilizers. The European Commission
(2002), for example, estimates γ ≈ 1/2 for Europe — a little more in
countries with an extensive social security system, a little less elsewhere.
And a similar relationship is thought to underlie UK’s fiscal policy (see
HMT, 2003: Boxes 5.2 and 6.2).
The expected signs of any remaining factors are not so clear. The debt
burden should increase current deficits, unless there is a systematic debt
reduction program underway. Inflation should have a positive impact on the
deficit ratio if fiscal policy is used for stabilization purposes, but it had no
effect otherwise. Finally, the output gap should also have a positive impact
on the deficit ratio, if the latter is being used for stabilization purposes —
in which case interest rates should be negatively correlated with the size
11 See Taylor (2000), Gali and Perotti (2003), Canzoneri (2004), and Turrini and in ‘t Veld
(2004) for similar formulations. The European Commission (2002) uses a similar rule, but
defines d>0 to be a deficit. They therefore expect γ to be negative.

80 Andrew Hughes Hallet
Table 2.
Fiscal policy reaction functions.
For the United Kingdom, sample period 1997q3–2004q2
d t =−0.444 + 0.845debt t + 0.0685r t + 1.076gap t
(0.37) (7.64) (0.30) (1.72)
For the Eurozone, sample period 1999q1–2004q2
d t = 3.36 + 1.477d t−1 − 0.740π
(2.96)
+9,21
e − 0.207r t − 0.337gap t
(9.66) (2.21) (1.16) (2.18)
R 2 = 0.78,
F 3,24 = 33.23
R 2 = 0.95,
F 4,11 = 54.55
Key: d t = gross deficit/GDP (%), where d

The Advantages of Fiscal Leadership in an Economy 81
Consequently, the United Kingdom appears to use fiscal policy for stabilization
in a minor way as claimed, while the Euro economies seem not
to use fiscal policy this way at all. Confirmation of this comes from the
responses to interest rate changes, which are positive but very small and
statistically insignificant in the United Kingdom, but negative and near significant
in Europe. This implies that the British fiscal policies are chosen
independently of the monetary policy, as suggested by our weak leadership
model. But, if there is any association at all, then both the fiscal and
monetary policies would be compliments and weakly co-ordinated.
The UK results are therefore inconclusive. They are consistent with
independent policies, or fiscal leadership — the latter, despite the insignificance
of the direct fiscal-monetary linkage, because of the significant output
gap term in the fiscal equation which, given the same effect is not found in
the monetary policy reactions, suggests fiscal leadership may in fact have
been operating. In any event, there is no suggestion of monetary leadership;
if anything happens, the results imply independence or fiscal leadership.
In the Eurozone, the results are quite different. Here, the significant
result is the conflict among instruments in monetary policy (and essentially
the same conflict in the fiscal policy reactions). Hence, the policies are
competitive, which suggests that they form a Nash equilibrium (or possibly
monetary leadership, since the coefficient on fiscal policy in the Taylor
rule is small and there is no output gap smoothing). This suggests weak
monetary leadership, or a simple non-co-operative game.
5. Theoretical Evidence: A Model of Fiscal Leadership
5.1. The Economic Model and Policy Constraints
The key question now is: would governments want to pursue fiscal precommitment?
Do they have an incentive to do so? And would there be a
clear improvement in terms of an economic performance if they did? More
important, would the fiscal leadership model be more advantageous, if fiscal
policy was limited by a deficit rule in the form of “hard” targets (as in the
original stability pact) or “soft” targets?
To answer these questions, we extend a model used in Hughes Hallett
and Weymark (2002; 2004a;b; 2005) to examine the problem of monetary
policy design when there are interactions with fiscal policy. For exposition
purposes, we suppress the spillovers among countries and focus on the
following three equations to represent the economic structure of any one

82 Andrew Hughes Hallet
country 13 :
π t = π e t + αy t + u t (3)
y t = β(m t − π t ) + γg t + ε t (4)
g t = m t + s(by t − τ t ) (5)
where π t is inflation in period t, y t is the growth in output (relative to trend)
in period t, and πt e represents the rate of inflation that the rational agents
expect to prevail in period t, conditional on the information available at the
time expectations are formed. Next, m t ,g t , and τ t represent the growth in
the money supply, government expenditures, and tax revenues in period t,
and u t and ε t are random disturbances, which are distributed independently
with zero mean and constant variance. All variables are deviations from
their steady-state (or equilibrium) growth paths, and we treat trend budget
variables as pre-committed and balanced. Deviations from the trend budget
are, therefore, the only discretionary fiscal policy choices available. The
coefficients α, β, γ, s, and b are all positive by assumption. The assumption
that γ is positive is sometimes controversial. 14 However, the short-run
impact multipliers derived from Taylor’s (1993a) multicountry estimation
provide an empirical support for this assumption (as does the HMT, 2003).
According to Eq. (3), inflation is increasing, as the rate of inflation predicted
by private agents and in output growth. Equation (4) indicates that
both monetary and fiscal policies have an impact on the output gap. The
micro-foundations of the aggregate supply Eq. (3), originally derived by
Lucas (1972; 1973), are well known. McCallum (1989) shows that aggregate
demand equation like Eq. (4) can be derived from a standard, multiperiod
utility-maximization problem.
Equation (5) describes the government’s budget constraint. In earlier
chapters, we allowed discretionary tax revenues to be used for
13 Technically, we assume a blockwise orthogonalization of the traditional multicountry
model to produce independent semi-reduced forms for each country. The disturbance terms
may, therefore, contain foreign variables, but they will have zero means so long as these
countries remain on their long-run (equilibrium) growth paths on average (all variables being
defined as deviations from their equilibrium growth paths).
14 Barro (1981) argues that government purchases have a contractionary impact on output.
Our model, by contrast, treats fiscal policy as important because: (i) fiscal policy is widely
used to achieve re-distributive and public service objectives; (ii) governments cannot precommit
monetary policy with any credibility if fiscal policy is not pre-committed (Dixit
and Lambertini, 2003), and (iii) Central Banks, and the ECB, in particular, worry intensely
about the impact of fiscal policy on inflation and financial stability (Dixit, 2001).

The Advantages of Fiscal Leadership in an Economy 83
re-distributive purposes only, but permitted discretionary expenditures for
enhancing output.We further assumed that there were two types of agents —
rich and poor — and that only the rich use their savings to buy government
bonds. Based on this view, b would be the proportion of pre-tax income
(output) going to the rich and s, the proportion of after-tax income that the
rich allocate to saving. Tax revenues, τ t , can then be used by the government
to re-distribute income from the rich to poor, either directly or via public
services. This structure, therefore, has output-enhancing expenditures g t ,
and discretionary transfers τ t . Both are financed by aggregate tax revenues;
that is, from discretionary and trend revenues. Expenditures above these
revenues must be financed by the sale of bonds.
5.2. An Alternative Interpretation
We could, however, take a completely different interpretation of Eq. (5).
We could take the term s(by t − τ t ) to be the proportion of the budget-deficit
ratio, as it currently exists, adjusted for the effect of growth on this ratio
and any discretionary taxes raised in this period, which the government
now proposes to spend in period t. The deficit ratio itself is of course
d = (G − T)/Y = (e − r), where G and T are the absolute levels of
government spending and tax revenues, and e and r are their counterparts as
a proportion of Y. If the economy grows, then d = (G−T)/Y −ẏ(e−r)
where ẏ denotes the growth rate in national income. If we wish to see what
would happen to this deficit ratio if fiscal policies were not changed, it
means new spending can only be allowed to take place out of new revenues
generated by growth: G = T = rY. Inserting this, we have d =
−(e − r)ẏ =−dẏ. Since y t is the deviation of Y from its steady-state
path, by t in Eq. (5) will equal d, the change in the existing deficit ratio
under existing expenditure plans and tax codes, if b =−(e − r)/Y 1 . The
government will spend some proportion of that, s, less new discretionary
taxes in the current period. Hence, s would typically equal 1, although it
might be less, if some parts were saved in social security funds or other
assets. This defines what would happen to the deficit ratio if there were no
change in existing fiscal policies; but the term in τ t shows that governments
may also raise additional taxes in order to reduce the current deficit ratio
to some desired target value, θ, say. This target is likely to be θ = 0, to
balance the budget over the cycle, as required by the stability pact. We give
governments such a target, in the form of either a soft or a hard rule, in the
objective functions that are discussed in Section 5.

84 Andrew Hughes Hallet
Given this new interpretation, we can now solve for πt e,π t, and y t from
Eqs. (3) and (4). This yields the following reduced forms:
[
π t (g t ,m t ) = (1 + αβ) −1 αβm t + αγg t + m e t + γ ]
β ge t + αε t + u t (6)
y t (g t ,m t ) = (1 + αβ) −1 [βm t + γg t − βm e t − γge t + ε t − βu t ]. (7)
Solving for τ t using Eqs. (5) and (7), then yields:
τ t (g t ,m t ) = [s(1 + αβ)] −1 [(1 + αβ + sbβ)m t − (1 + αβ − sbγ)g t
− sbβm e t − sbγge t + sb(ε t − βu t )]. (8)
5.3. Government and Central Bank Objectives
In our formulation, we allow for the possibility that the government and
an independent central bank may differ in their objectives. In particular,
we assume that the government cares about inflation stabilization, output
growth, and the provision of public services (and hence the size of the public
sector deficit or debt); whereas the central bank, if left to itself, would be
concerned only with the first two objectives, 15 and possibly only the first
one. We also assume that the government has been elected by majority
vote, so that the government’s loss function reflects society’s preferences
to a significant extent.
Formally, the government’s loss function is given by:
L g t = 1 2 (π t −ˆπ) 2 − λ g 1 y t + λg 2
2 [(b − θ)y t − τ t ] 2 (9)
where ˆπ is the government’s inflation target, λ g 1
is the relative weight or
importance that the government assigns to output growth, 16 and λ g 2
is the
relative weight, which it assigns to the debt or deficit rule. The parameter θ
represents the target value for the debt or deficit to the GDP ratio, which the
government would like to reach: hence (b − θ)y t becomes the target for its
15 Since the central bank has no instruments to control the debt itself, it can only react to
poor fiscal discipline indirectly: e.g., to the extent that its inflation objective is compromised,
where it does have an instrument.
16 Barro and Gordon (1983) also adopt a linear output target. In the delegation literature, the
output component in the government’s loss function is usually represented as quadratic to
reflect an output stability objective. In our model, the quadratic term in debt/deficits allows
monetary and fiscal policy to play a stabilization role as well as pick a position on the
economy’s output-inflation trade-off.

The Advantages of Fiscal Leadership in an Economy 85
discretionary revenues, τ t . All the other variables are as previously defined.
We may regard large values of λ g 2 , say λg 2 > max[1,λg 1
], as defining a
“hard” debt or deficit rule; and smaller values, λ g 2 < min[1,λg 1
], as a “soft”
debt or deficit rule.
The objectives of the central bank, however, may be quite different from
those of the government. We model them as follows:
L cb
t
= 1 2 (π −ˆπ)2 − (1 − δ)λ cb y t − δλ g 1 y t
+ δλg 2
2 [(b − θ)y t − τ t ] 2 (10)
where 0 ≤ δ ≤ 1, and λ cb is the weight, which the central bank assigns
to the output growth. The parameter δ measures the degree to which the
central bank is forced to take the government’s objectives into account.
The closer δ is to 0, the greater is the independence of the central bank in
making its choices. And the lower is λ cb is, the greater is the degree of its
conservatism in making these choices.
In Eq. (9), we have defined the government’s inflation target as ˆπ. The
fact that the same inflation target appears in Eq. (10) would be correct for
the cases where the bank has the instrument independence, but not target
independence. However, it is easy to relax this assumption and allow the
central bank to choose its own target, as the ECB does. But, as I show in
Hughes Hallett (2005), there is no advantage in doing so since the government
would simply adjust its parameters to compensate. Hence, only if the
bank is free to choose the value of λ cb as well, do we get an extra advantage.
Yet, even this will not be enough to outweigh the advantages to be gained
from fiscal leadership — for the reasons noted in Section 5.
A second feature is that Eqs. (9) and (10) specify symmetric inflation
targets around ˆπ. Symmetric inflation targets are particularly emphasized
as being required of both monetary policy and the fiscal authorities (HMT,
2003). We have, therefore, specified both to be features of the government
and the central bank objective functions here. However, it is not clear that
symmetry has been a feature of the European policy making in practice.
Indeed, the ECB has acquired a reputation for being more concerned to
tighten monetary policy when π> ˆπ, than it is to loosen it when π< ˆπ.
Consequently, rather than symmetry in the output-gap target, we have
asymmetric penalties, which tighten the fiscal constraints in recessions,
but weaken them in a boom when the debt and deficits would be falling
anyway. On one hand, this might not be ideal, since it introduces an element
of pro-cyclicality; on the other hand, it brings the rule closer to reality.

86 Andrew Hughes Hallet
5.4. Institutional Design and Policy Choices
We characterize the strategic interaction between the government and the
central bank as a two-stage non-co-operative game in which the structure of
the model and the objective functions are common knowledge. In the first
stage, the government chooses the institutional parameters δ and λ cb . The
second stage is a Stackelberg game in which fiscal policy takes on a leadership
role. In this stage, the government and the monetary authority set their
policy instruments, given the δ and λ cb values determined at the previous
stage. Private agents understand the game and form rational expectations
for future prices in the second stage. Formally, the policy game runs as
follows:
5.4.1. Stage 1
The government solves the problem:
{ 1
min ELg (g t, m t, δ, λ cb ) = E
δ,λ cb 2 [π t(g t ,m t ) −ˆπ] 2 − λ 2 1 [y t(g t ,m t )]}
+ λg 2
2 E[(b − θ)y t(g t ,m t ) − τ t (g t ,m t )] 2 (11)
where L g (g t ,m t ,δ,λ cb ) is Eq. (9) evaluated at (g t ,m t ,δ,λ cb ), and E
denotes expectations.
5.4.2. Stage 2
(a) Private agents form rational expectations about future prices πt e, before
the shocks u t and ε t are realized.
(b) The shocks u t and ε t are realized and observed by both the government
and the central bank.
(c) The government chooses g t , before m t is chosen by the central bank,
to minimize L g (g t ,m t , ¯δ, ¯λ cb ) where ¯δ and ¯λ cb are at the values determined
at stage 1.
(d) The central bank then chooses m t , taking g t as given, to minimize:
L cb (g t ,m t , ¯δ, ¯λ cb ) = (1 − ¯δ)
[π t (g t ,m t ) −ˆπ] 2
2
− (1 − ¯δ)¯λ cb [y t (g t ,m t )] + ¯δL g (g t ,m t , ¯δ, ¯λ cb )
(12)

The Advantages of Fiscal Leadership in an Economy 87
We solve this game by solving the second stage (for the policy choices)
first, and then substituting the results back into Eq. (11) to determine the
optimal operating parameters δ and λ cb . From stage 2, we get:
π t (δ, λ cb ) =ˆπ + (1 − δ)β(φ − η)λcb + δ(βφ + γ)λ g 1
α[β(φ − η) + δ(βη + γ)]
(13)
y t (δ, λ cb ) =−u t /α (14)
where
τ t (δ, λ cb ) = (1 − δ)βs(βη + γ)(λcb − λ g 1 )
[β(φ − η) + δ(βη + γ)]λ 9 − (b − θ)u t
α
2
η = ∂m t
∂g t
= −α2 γβs 2 + δφλ g 2
(αβs) 2 + δ 2 λ g 2
(15)
(16)
φ = 1 + αβ − γθs (17)
and
= 1 + αβ + βθs. (18)
Evidently, is positive. We assume φ to be positive as well. One would
certainly expect φ>0 since, with θ0.
Nevertheless, the conflict which stands revealed within the fiscal policy is
important. In order to get φ0.

88 Andrew Hughes Hallet
Substituting Eqs. (13)–(15) back into Eq. (11), we can now get the
stage 1 solution from:
{
min ELg (δ, λ cb ) = 1 (1 − δ)β(φ − η)λ cb + δ(βφ + γ)λ g } 2
1
δ,λ cb 2 α[β(φ − η) + δ(βη + γ)]
{
+ λg 2 (1 − δ)βs(βη + γ)(λ cb − λ g 1 )
} 2
2 [β(φ − η) + δ(βη + γ)]λ g . (19)
2
This part of the problem has first-order conditions:
and
(1 − δ)(φ − η)λ g 2 {(1 − δ)β(φ − η)λcb + δ(βφ + γ)λ g 1 }
−(1 − δ) 2 (βη + γ) 2 α 2 s 2 β(λ g 1 − λcb ) = 0 (20)
{(1 − δ)β(φ − η)λ cb + δ(βφ + γ)λ g 1 }
× (λ g 1 − λcb ) {δ(1 − δ) + (φ − η)} λ g 2
−(1 − δ)(βη + γ)α 2 s 2 β {(βη + γ) − (1 − δ)β} (λ g 1 − λcb ) 2 = 0.
(21)
where = ∂η/∂δ. There are two real-valued solutions which satisfy this
pair of first-order conditions. 19 Both are satisfied when δ = 1 and λ cb = λ g 1 .
This solution describes a fully dependent central bank, which is not appropriate
in the Eurozone case. And, it turns out to be inferior to the second
solution: δ = λ cb = 0. In this solution, the central bank is fully independent
and exclusively concerned with the economy’s inflation performance.
Out of the two possibilities, the solution which yields the lowest welfare
loss, as measured by the government’s (society’s) loss function, can be
identified by comparing Eq. (19) to the expected loss that would be suffered
under the alternative institutional arrangement. Substituting, δ = 1 and
λ cb = λ g 1 in Eq. (19) results in: EL g = (λg 1 )2
2α 2 . (22)
19 Because η is a function of δ, Eq. (21) is quartic in δ. This polynomial has four distinct
roots, of which only two are real-valued. The complete solution may be found in Hughes
Hallett and Weymark (2002).

The Advantages of Fiscal Leadership in an Economy 89
But substituting, δ = λ cb = 0 in the right-hand-side of Eq. (19) yields:
EL g = 0. (23)
Consequently, our results show that, when there is fiscal leadership, society’s
welfare loss (as measured by Eq. (19)) is minimized when the government
appoints independent central bankers who are concerned only with
the achievement of a mandated inflation target and completely disregard
the impact their policies may have on the output.
However, our results also indicate that fiscal leadership with an independent
central bank can be beneficial under more general conditions. When
δ = 0, βη + γ = 0 and the externalities between policy makers are neutralized.
20 As a result, Eq. (19) will become:
{ λ
cb
} 2
(24)
EL g = 1 2
α
for any value of λ cb . Hence, an independent central bank will always produce
better results than a dependent one, so long as it is more conservative
than the government (λ cb

90 Andrew Hughes Hallet
This is always smaller than the loss incurred when fiscal leadership is combined
with a dependent central bank. However, the optimal degree of conservatism
for an independent central bank, in this case, is obtained by setting
δ = 0 in Eq. (25) to yield:
λ cb∗ = (αγs)2 λ g 1
(αγs) 2 + φ 2 λ g . (27)
2
It is straightforward to show that the value of EL g in Eq. (24) is always
less than Eq. (26) as long as:
λ cb < [λ g 1 λcb∗ ] 1/2 . (28)
It is also evident that λ cb∗ 0. Consequently, fiscal leadership
with any λ cb

The Advantages of Fiscal Leadership in an Economy 91
Comparing these two sets of outcomes, we have five conclusions. These
conclusions signify the main results of this paper:
(a) Fiscal leadership eliminates the inflationary bias, and results in lower
inflation without any loss in output or output volatility. The proximate
cause of this surprising result is that optimization under fiscal leadership
leads to higher taxes and larger debt repayments. 22
(b) The deeper reason is that there is a self-limiting aspect to the longrun
design of fiscal policy. Unless the effect of fiscal policy on output
is so large as to generate savings/taxes that could finance both fiscal
expansions and debt re-payments (this possibility is ruled out in the
deficit rule case), each expansion designed to increase output would
simply be accompanied by a greater burden of debt. Hence, in order to
preserve the long-run sustainability of its finances, the government must
eventually raise taxes. This fact takes some inflationary pressure off the
central bank when fiscal expansions are called for. As a result, the bank
is less likely to tighten the monetary policy, and externalities are reduced
on both sides. This is what generates a better co-ordination between
the policy makers, as noted in Section 5. But, this can only happen
if the government has a genuine commitment to the long-run goals
(sustainable public finances, and a debt or deficit rule in this case), since
only then will the fiscal policy leader take into account the predictable
reactions (of the follower) to any short-run deviations by the leader.
The follower knows that the leader is not likely to sacrifice his long-run
goals by making such deviations (and anyway has the opportunity to
clear up the mess, according to the follower’s own preferences, if the
leader does so). Thus, in the short-run under simultaneous moves, each
player fails to consider the predictable response, and costs, which the
externalities he/she imposes on his/her rival would create. The ability to
co-ordinate would be lost, and the outcomes worse for both. We show
this in Section 5 (and in a more formal analysis in Hughes Hallett,
2005).
(c) These results hold independently of the commitment to the debt rule
(λ g 2
), or its target value (θ), and independently of the government’s preference
to stabilize or spend (λ g 1
,s), and of the economy’s transmission
parameters (α,β,γ)or the particular value of b as discussed above.
22 Taxes are lower under simultaneous moves because λ cb

92 Andrew Hughes Hallet
(d) Since Eτt ∗ < 0 in Eq. (32), but Eτ t = 0 in (29), the simultaneous moves
regime will always end up in increasing the deficit levels. Therefore, it
will eventually exceed any limit set for the debt ratio. Fiscal leadership
will do neither of these things. More generally, the simultaneous moves
game always leads to fiscal expansions if money financing is small. 23
Indeed, the expected value of s(byt
∗ − τt ∗ ) in Eq. (5) is zero under
fiscal leadership, but φλ cb∗ /(α 2 γ) > 0 in the simultaneous moves case
(as expected, since the monetary policy externalities would be larger).
And since revenues are lower in the latter case, budget deficits are
larger. Hence, the gains from the fiscal leadership are more than just
better outcomes. Leadership also implies less expansionary budgets
and tighter public expenditure controls. The ECB should find this a
significantly more comfortable environment to operate in.
(e) The simultaneous moves regime approaches fiscal leadership, as the
debt rule becomes progressively “harder”: that is, EL g → 0,λ cb∗ →
0; πt ∗ →ˆπ, and Eτt ∗ → 0, as λ g 2 →∞.
6. The Co-Ordination Effect
In our model, the central bank is independent. Without further institutional
restraints, interactions between an independent central bank and the government
would lead to non-co-operative outcomes. But, if the government
is committed to long-term leadership in the manner that I have described,
the policy game will become an example of rule-based co-ordination in
which both parties can gain without any reduction in the central bank’s
independence. However, this is not to say that both parties gain equally. If
the inflation target is strengthened after the fiscal policy is set, the leadership
gains to the government will be less (Hughes Hallett and Viegi, 2002). This
is an important point because it implies that granting leadership to a central
bank whose inflation aversion is already greater than the government’s, or
whose commitment is greater, will produce no additional gains. For this
reason, granting leadership to a central bank that cannot influence debt or
deficit directly, but puts a higher priority on inflation control will bring
smaller gains from a society’s point of view (whatever it may do for the
central bank). I demonstrate these points formally in Hughes Hallett (2005).
23 m t ≈ 0; see Appendix B. This result still holds good when β>γ, even if monetary
financing is allowed. It also holds good if the central bank is conservative, or the government
is liberal, when β

The Advantages of Fiscal Leadership in an Economy 93
Finally, given the structure of the Stackelberg game, there is no incentive
to re-optimize for either party — so long as the government remains
committed to long-term leadership rather than short-term demand management
— unless both parties agree to reduce their independence through
discretionary co-ordination. 24 This is a general result: it holds good for any
model where both inflation and output depend on both monetary and fiscal
policy, and where inflation is targeted to some degree by both players
(Demertzis et al., 2004; Hughes Hallett and Viegi, 2002). Thus, although
Pareto improvements, over no co-operation, do not emerge for both parties
in all Stackelberg games, they do so in problems of the kind examined here.
Our results are robust.
6.1. Empirical Evidence
Whether or not these results are of practical importance is another matter.
In Table 3, I have computed the expected losses under the simultaneous
move and fiscal leadership regimes for 10 countries when both fiscal policy
and the central bank are constructed optimally. The data I have used is from
1998, the year in which the Eurozone was created. The data itself, and its
sources, are summarized in Appendix A.
The countries that are selected fall into three groups:
(a) Eurozone countries, with independently set fiscal and monetary policies
and target independence: France, Germany, Italy, and the Netherlands;
(b) Explicit inflation targeters with fiscal leadership: Sweden, New
Zealand, and the United Kingdom and
(c) Federalists, with joint inflation and stabilization objectives: United
States, Canada, and Switzerland.
In the first group, monetary policy is conducted at the European level
and fiscal policy at the national level. Policy interactions, in this group,
can be characterized in terms of a simultaneous move game, with target as
well as with instrument independence for both sets of policy authorities.
24 This supplies the political economy of our results. We need no pre-commitment beyond
leadership (the Stackelberg game supplies sub-game perfection, see Note 4) and no punishment
beyond electoral results. The former will hold so long as governments have a natural
commitment to maintaining sustainable public finances, public services (health, education,
and defence), or social equity, all long-run “contractual” issues. The latter will then arise
from the political competition inherent in any democracy.

94 Andrew Hughes Hallet
Table 3.
Expected losses under a deficit rule, leadership vs. other strategies.
Full Fiscal Simultaneous Losses under
dependence leadership moves simultaneous
δ = 1 δ = 0; λ g 1 = 1 1 = 1 moves: Growth-
λ cb = λ g 1 λ cb = 0
λ cb = λ cb∗ rate equivalents
France 5.78 0.00 0.134 13.4
Germany 16.14 0.00 0.053 5.30
Italy 1.28 0.00 0.207 20.7
Netherlands 1.28 0.00 0.165 16.5
Sweden 4.51 0.00 0.034 3.40
New Zealand 8.40 0.00 0.071 7.10
United Kingdom 3.37 0.00 0.057 5.70
United States 6.46 0.00 0.248 24.8
of America
Canada 12.50 0.00 0.118 11.8
Switzerland 4.79 0.00 0.066 6.60
It is, perhaps, arguable that the Eurozone has adopted a monetary leadership
regime; but the empirical evidence for this was weak, and the fiscal
constraints that could have sustained such a leadership were widely ignored.
The second group of countries has adopted explicit, and mostly publicly
announced, inflation targets. Central banks in these countries have
been granted instrument independence, but not target independence. The
government either sets, or helps to set, the inflation target. In each case, the
government has adopted long-term (supply side) fiscal policies, leaving an
active demand management to monetary policy. These are clear cases in
which there is both fiscal leadership and instrument independence for the
central bank.
The third group represents a set of more flexible economies, with
implicit inflation targeting and a statutory concern for stabilization; also federalism
in fiscal policy and independence at the central bank, and therefore
no declared leadership in either fiscal or monetary policies. This provides
a useful benchmark for the other two groups.
The performance under the different fiscal regimes when the fiscal constraint
is a relatively soft deficit rule is reported in Table 3. Column 1
shows the losses under a dependent central bank in welfare units — leadership
or not. Column 2 reflects the losses that would be incurred under

The Advantages of Fiscal Leadership in an Economy 95
the government leadership with an independent central bank that directs
monetary policy exclusively towards the achievement of the inflation target
(i.e., δ = λ cb = 0). The third column gives the minimum loss associated
with a simultaneous decision-making version of the same game. In each
case, the deficit rule is soft for the Eurozone countries (λ g 2
= 0.25); medium
strength for the United States, Canada, and Switzerland (λ g 2
= 0.5); and
harder for Sweden, the United Kingdom and New Zealand (λ g 2
= 1). The
deficit ratio targets are 0% in all countries (a balanced budget in the medium
term), but the propensity to spend, s, out of any remaining deficit or any
endogenous budget improvements is one.
Evidently, complete dependence in monetary policy is extremely unfavorable,
although the magnitude of the loss varies considerably from country
to country. The losses in Column 3 (Table 3) appear to be relatively small
in comparison. However, when these figures are converted into “growth-rate
equivalents”, I find these losses to be significant. A growth-rate equivalent
is the loss in output growth that would produce the same welfare loss, if all
other variables remain fixed at their optimized values. 25
The figures in Column 4 are more interesting. They show that the losses
associated with simultaneous decision-making are equivalent to having permanent
reductions of up to 20% in the level of national income. That is,
France, Italy, and the Netherlands could have expected to have grown about
15%–20% more, had they adopted fiscal leadership with deficit targets; and
Sweden, the United Kingdom, and New Zealand around 3%–5% less, had
they not done so. Similarly, fiscal leadership with debt targeting would
be worth 10%–20% extra GDP in the United States, and Canada. These
are significant gains and significantly larger than could be expected from
international policy co-ordination itself (Currie et al., 1989).
Thus, the immediate effect of introducing a stability pact deficit rule
has been to increase the costs of an unco-ordinated (simultaneous moves)
regime dramatically. This reveals the weakness of the deficit rule as a
25 Currie et al. (1989). To obtain these figures, I compute the marginal rates of transformation
around each government’s indifference curve to find the change in output growth, dy t , that
would yield the welfare losses in Column 3. Formally,
dy t =
dEL g t
[λ g 2 {(b − θ)y t − τ t }(b − θ) − λ g 1 ]
using Eq. (9). The minimum value of dy t is, therefore, attained when tax revenues τ t grow at
the same rate as the re-payment target (b − θ)y t . These are the losses reported in Column 4.

96 Andrew Hughes Hallet
restraint mechanism. Because it is a flow and not a stock, it has no inherent
persistence. Moreover, a larger part (the current automatic stabilizers,
social expenditures, and tax revenues) will be endogenous, varying with the
level of economic activity and with the pressures of the electoral cycle. It is,
therefore, much harder to use as a commitment device with any credibility
in the long term. If we assume that it can be pre-committed, as in the leadership
scenario, then we get good results of course. But, if this assumption
is likely to be violated (or challenged), then the fact that the results are so
much worse than in the simultaneous moves case shows how difficult it
is to pre-commit deficits in advance. Being only a small component in a
moving total, it does not have the persistence of a cumulated debt criterion
because violations are not carried forward. So, when policy conflicts arise,
the deficit either fails its target or it has to be restrained to such a degree
that it starts to do serious damage to overall economic performance.
7. Conclusions
I conclude this chapter with the following observations:
(a) Fiscal leadership leads to improved outcomes because it implies a
degree of co-ordination and reduced conflicts between institutions,
without the central bank having to lose its ability to act independently.
This places the outcomes somewhere between the superior (but discretionary)
policies of complete co-operation; and the non-co-operative
(or rule-based) policies of complete independence.
(b) The co-ordination gains come from the self-limiting action of fiscal
policy when fiscal policy is given a long-run focus in the form of a
(soft) debt or deficit rule. Leadership is the crucial element here; these
gains do not appear in a straight-forward competitive regime with the
same debt or deficit rule.
(c) The leadership model predicts improvements in inflation and the fiscal
targets, without any loss in growth or output volatility. In addition,
leadership requires less precision in the setting of the strategic or institutional
parameters. It is easier to implement.
(d) Debt ratios will increase in a policy game without co-ordination, but
do not do so under fiscal leadership. Likewise, deficit rules without
co-ordination to restrain fiscal policy imply larger deficits (and more
expansionary policies) than do debt rules of a similar specification
because deficits (being a flow not a stock, and with less natural persistence)
are less easy to pre-commit credibly. These two results explain

The Advantages of Fiscal Leadership in an Economy 97
why the ECB prefers hard restraints (and why the fiscal policy makers
do not), and suggests that the ECB may actually prefer fiscal leadership
because of the greater degree of pre-commitment implied.
References
Barro, RJ (1981). Output effects of government purchases. Journal of Political Economy
89, 1086–1121.
Barro, RJ and DB Gordon (1983). Rules, discretion, and reputation in a model of monetary
policy. Journal of Monetary Economics 12, 101–121.
Basar, T (1989). Time consistency and robustness of equilibria in non-cooperative dynamic
games. In Dynamic Policy Games in Economics, F van der Ploeg and A de Zeeuw
(eds.), pp. 9–54. Amsterdam: North Holland.
Basar, T and G Olsder (1989). Dynamic noncooperative game theory. In Classics in Applied
Mathematics, SIAM series, Philadelphia: SIAM.
Brandsma, A and A Hughes Hallett (1984). Economic conflict and the solution of dynamic
games. European Economic Review 26, 13–32.
Buti, M, S Eijffinger and D Franco (2003). Revisiting the stability and growth pact: grand
design or internal adjustment? Discussion Paper 3692. London: Centre for Economic
Policy Research.
Canzoneri, M (2004). A New View on The Transatlantic Transmission of Fiscal Policy
and Macroeconomic Policy Coordination. In The Transatlantic Transmission of Fiscal
Policy and Macroeconomic Policy Coordination, M Buti (ed.), Cambridge: Cambridge
University Press.
Currie, DA, G Holtham andA Hughes Hallett (1989). The theory and practice of international
economic policy coordination: does coordination pay? In Macroeconomic Policies in
an Interdependent World, R Bryant, D Currie, J Frenkel, P Masson and R Portes (eds.),
Washington, DC: International Monetary Fund, 125–148.
Demertzis, M, A Hughes Hallett and N Yiegi (2004). An Independent Central Bank Faced
with Elected Governments: A Political Economy Conflict. In European Journal of
Political Economy 20(4), 907–922.
Dieppe, A, K Kuster and P McAdam (2004). Optimal monetary policy rules for the Euro
Area: an analysis using the area wide model. Working Paper 360. Frankfurt: European
Central Bank.
Dixit,A (2001). Games of monetary and fiscal interactions in the EMU. European Economic
Review 45, 589–613.
Dixit, AK and L Lambertini (2003). Interactions of commitment and discretion in monetary
and fiscal issues. American Economic Review 93, 1522–1542.
Dow, JCR (1964). The Management of the British Economy 1945–1960. Cambridge:
Cambridge University Press.
European Commission (2002). Public finances in EMU:2002. European Economy: Studies
and Reports 4, Brussels: European Commission.
Fatas, A, J von Hagen, A Hughes Hallett, R Strauch and A Sibert (2003). Stability and
Growth in Europe. London: Centre for Economic Policy Research (MEI-13).
Gali, J and R Perotti (2003). Fiscal policy and monetary integration in Europe. Economic
Policy 37, 533–571.

98 Andrew Hughes Hallet
HM Treasury (HMT) (2003). Fiscal Stabilization and EMU. HM Stationary Office, Cmnd
799373. Norwich: also available from www.hm-treasury.gov.uk.
Hughes Hallett, A (1984). Noncooperative strategies for dynamic policy games and the
problem of time inconsistency. Oxford Economic Papers 36, 381–399.
Hughes Hallett,A (2005). In praise of fiscal restraint and debt rules: what the Euro zone might
do now. Discussion Paper 5043. London: Centre for Economic Research, 251–279.
Hughes Hallett, A and D Weymark (2002). Government leadership and central bank design.
Discussion Paper 3395, London: Centre for Economic Research.
Hughes Hallett, A and N Viegi (2002). Inflation targeting as a coordination device. Open
Economies Review 13, 341–362.
Hughes Hallett, A and D Weymark (2004a). Policy games and the optimal design of central
banks. In Money Matters, P Minford (ed.). London: Edward Elgar.
Hughes Hallett,A and DWeymark (2004b). Independent monetary policies and social equity.
Economics Letters 85, 103–110.
Hughes Hallett,A and D Weymark (2005). Independence before conservatism: transparency,
politics and central bank design. German Economic Review 6, 1–25.
Lucas, RE (1972). Expectations and the neutrality of money. Journal of Economic Theory
4, 103–124.
Lucas, RE (1973). Some international evidence on output-inflation trade-offs. American
Economic Review 63, 326–334.
McCallum, BT (1989). Monetary Economics: Theory and Policy. New York: Macmillan.
Svensson, L (2003). What is wrong with Taylor rules? Using judgement in monetary rules
through targeting rules. Journal of Economic Literature 41, 426–477.
Taylor, JB (1993a). Macroeconomic Policy in a World Economy: From Econometric Design
to Practical Operation. New York: W.W. Norton and Company.
Taylor, JB (1993b). Discretion vs. policy rules in practice. Carnegie-Rochester Conference
Series on Public Policy 39, 195–214.
Taylor, JB (2000). Discretionary fiscal policies. Journal of Economic Perspectives 14, 1–23.
Turrini, A and J in ‘t Veld (2004). The Impact of the EU Fiscal Framework on Economic
Activity. DGII, Brussels: European Commission.
Appendix A: Data Sources for Table 3
The data used in Table 3 are set out in the table below. They come from different
sources and represent “stylized facts” for the corresponding parameters.
The Phillips curve parameter, α, is the inverse of the annualized
sacrifice ratios on quarterly data from 1971–1998. The values for β and γ,
the impact multipliers for fiscal and monetary policy, respectively, are the
one-year simulated multipliers for these policies in Taylor’s multicountry
model (Taylor, 1993a). I have calibrated the remaining parameters using
stylized facts from 1998: the year that EMU started, and the year that new
fiscal and monetary regimes took effect in the United Kingdom and Sweden.
Thus, s is the automatic stablizer effect on output according to the European
Commission (2002) and HMT (2003) estimates, allowing for larger social

The Advantages of Fiscal Leadership in an Economy 99
Table 4.
Data for the deficit rule calculations.
α β γ s θ φ λ g 2
France 0.294 0.500 0.570 1 0 1.147 0.25
Germany 0.176 0.533 0.430 1 0 1.094 0.25
Italy 0.625 0.433 0.600 1 0 1.271 0.25
Netherlands 0.625 0.489 0.533 1 0 1.306 0.25
Sweden 0.333 0.489 0.533 1 0 1.163 1
New Zealand 0.244 0.400 0.850 1 0 1.098 1
UK 0.385 0.133 0.580 1 0 1.038 1
United States 0.278 0.467 1.150 1 0 1.130 0.5
Canada 0.200 0.400 0.850 1 0 1.080 0.5
Switzerland 0.323 0.489 0.533 1 0 1.158 0.5
security sectors in the Netherlands and Sweden. Similarly, θ is set to give a
debt target somewhat below each country’s 1998 debt ratio and the SGP’s
60% limit. Likewise, λ g 2
was set to imply a low, high, or medium commitment
to debt/deficit limits, as reflected in actual behavior in 2004. Finally,
I have set λ g 1
= 1 in each country to suggest that governments, if left to
themselves, are equally concerned about inflation and output stabilization.
For Table 4, I suppose that the deficit that remains after growth effects
and new discretionary taxes are accounted for will be spent (s = 1), and
that the medium-term deficit target is zero (θ = 0).
Appendix B: Derivation of the Change in Fiscal Stance
Between Regimes
The expected value of s(by t − τ t ) under fiscal leadership and simultaneous
moves can be obtained by inserting values first from Eq. (29), and then from
Eqs. (31) and (32), respectively. Taking the expected values, this yields
zero and φλ cb∗ /(α 2 γ) > 0 in each case. Applying this result to Eq. (4),
it shows that the expected change in output between regimes, which we
know to be zero, is (β − γ)m − βλ cb∗ /(αλ g 1
) + γ[s(by − τ)] = 0.
Hence,
m ={γ[s(by − τ)] + βλ cb∗ /(αλ g 1
)}/(β − γ)
which, given the change in s(by t − τ t ), is positive, if β>γ. In this case,
the simultaneous move regime is unambiguously more expansionary, and
will run larger deficits, than a regime with fiscal leadership. But, since

100 Andrew Hughes Hallet
γ/(β − γ) > 1, this result may not follow if β

Topic 2
Cheap-Talk Multiple Equilibria and Pareto —
Improvement in an Environmental
Taxation Games
Chirstophe Deissenberg
UniversitédelaMéditerranée and GREQAM, France
Pavel Ševčík
Universilé de Montréal, Canada
1. Introduction
The use of taxes as regulatory instrument in environmental economics is a
classic topic. In a nutshell, the need for regulation usually arises because
producing causes detrimental emissions. Due to the lack of a proper market,
the firms do not internalize the impact of these emissions on the utility of
other agents. Thus, they take their decisions on the basis of prices that do not
reflect the true social costs of their production. Taxes can be used to modify
the prices, confronting the firms so that the socially desirable decisions are
taken. The problem has been exhaustively investigated in static settings,
where there is no room for strategic interaction between the regulator and
the firms.
Consider, however, the following situations:
(1) The emission taxes have a dual effect, they incite the firms to reduce
production and to undertake investments in abatement technology. This
is typically the case, when the emissions are increasing in the output
and decreasing in the abatement technology;
(2) Emission reduction is socially desirable. The reduction of production
is not and
(3) The investments are irreversible. In this case, the regulator must find
an optimal compromise between implementing high taxes to motivate
high investments, and keeping the taxes low to encourage production.
101

102 Chirstophe Deissenberg and Pavel Ševčík
The fact that the investments are irreversible introduces a strategic
element in the problem. If the firms are naïve and believe his announcements,
the regulatory can insure high production and important investments
by first declaring high taxes and reducing them, once the corresponding
investments have been realized. More sophisticated firms, however, recognize
that the initially high taxes will not be implemented, and are reluctant
to invest in the first place. In other words, one is confronted with a typical
time inconsistency problem, which has been extensively treated in the monetary
policy literature following Kydland and Prescott (1977) and Barro and
Gordon (1983). In environmental economics, the time inconsistency problem
has received yet only limited attention, although it frequently occurs.
See among others Gersbach and Glazer (1999) for a number of examples
and for an interesting model, see Abrego and Perroni (1999); Batabyal
(1996a;b); Dijkstra (2002); Marsiliani and Renstrom (2000) and Petrakis
and Xepapadeas (2003).
The time inconsistency is directly related to the fact that the situation
described above, defines a Stackelberg game between the regulator (the
leader) and the firms (the followers). As noted in the seminal work of
Simaan and Cruz (1973a;b), inconsistency arises because the Stackelberg
equilibrium is not defined by mutual best responses. It implies that the
follower uses a best response in reaction to the leader’s action, but not that
the leader’s actions is itself a best response to the follower’s. This opens
the door to a re-optimization by the leader once the follower has played.
Thus, a regulator, who announces that it will implement the Stackelberg
solution, is not credible. An usual conclusion is that, in the absence of
additional mechanisms, the economy is doomed to converge towards the
less desirable Nash solution.
A number of options to insure credible solutions have been considered
in the literature — credible binding commitments by the Stackelberg
leader, reputation building, use of trigger strategies by the followers, etc.
(see McCallum (1997), for a review in a monetary policy context). Schematically,
these solutions aim at assuring the time consistency of Stackelberg
solution with either the regulator or the firms as a leader. Usually, these
solutions are not efficient and can be Pareto-improved.
In Dawid et al. (2005), we demonstrated the usefulness of a new solution
to the time inconsistency problem in environmental policy. We showed
that tax announcements, that are not respected, can increase the payoff not
only of the regulator, but also of all firms, if these include any number
of naïve believers who take the announcements at face value. Moreover,
if firms tend to adopt the behavior of the most successful ones, a unique

Cheap-talk Multiple Equilibria and Pareto 103
stable equilibrium may exist where a positive fraction of firms are believers.
This equilibrium Pareto-dominates the one, where all firms anticipate
perfectly the Regulator’s action. To attain the superior equilibrium, the
regulator builds reputation and leadership by making announcements and
implementing taxes in a way that generates good results for the believers,
rather than by pre-committing to his announcements.
The potential usefulness of employing misleading announcements to
Pareto-improve, upon standard game-theoretic equilibrium solutions was
suggested for the case of general linear-quadratic dynamic games in Vallee
et al. (1999) and developed by the same authors in subsequent papers.
An early application to environmental economies is Vallee (1998). The
believers/non-believers dichotomy was introduced by Deissenberg and
Gonzalez (2002), who study the credibility problem in monetary economics
in a discrete-time framework with reinforcement learning. A similar monetary
policy problem has been investigated by Dawid and Deissenberg (2005)
in a continuous-time setting akin to the used in the present work.
In this chapter, we re-visit the model proposed by Dawid et al. (2005)
and show that a minor (and plausible) modification of the regulator’s objective
function, opens the door to the existence of multiple stable equilibria
with distinct basins of attraction — with important interpretations and
potential consequences for the practical conduct of environmental policy.
This chapter is organized as follows. In Section 2, we present the model
of environmental taxation and introduce the imitation-type dynamics that
determinate the evolution of the number to believers in the economy. In
Section 3, we derive and discuss the solution of the sequential Nash game,
one obtains by assuming a constant proportion of believers. In Section 4,
we formulate the dynamic problem and investigate its solution numerically.
Finally, in Section 6, we summarize the mechanisms at work in the model
and the main insights.
2. The Model
We consider an economy, consisting of a Regulator R and a continuum of
atomistic, profit-maximizing firms i with an identical production technology.
Time τ is continuous. To keep the notation simple, we do not index
the variables with either i or r unless it is useful for a better understanding.
In a nutshell, the situation of interest is the following: The regulator
can tax the firms to incite them to reduce their emission, and to generate
tax income, taxes, however, have a negative impact on the employment

104 Chirstophe Deissenberg and Pavel Ševčík
(and thus, on the labor income) and the profits. Thus, R has to choose the
tax level in order to achieve an optimal compromise among tax revenue,
private sector income, emission reduction, and employment levels. The
following sequence of event (S) occurs in every τ:
— R makes a non-binding announcement t a ≥ 0 about the tax level t ≥ 0
it will choose.
—Givent a , the firms form expectations t e about the true level of the
environmental tax. As will be described in more detail later, there are
two different ways for an individual firm to form its expectations.
— Each firm decides about its level of investment v based on its expectation
t e .
— R choose the actual level of tax t ≥ 0. The tax level t is the amount
each firm has to pay per unit of its emissions.
— Each firm produces a quantity x.
— Each firm may revise the way it forms its expectations depending on its
relative profits.
All firms are identical, except for the way they form their expectations t e .
We assume full information: the regulator and the firms perfectly know
both the sequence, we just presented and the economic structure will be
(production and prediction technology, objective functions ...) described
in the remainder of this section.
2.1. The Firms, Bs and NBs
Each firm produces the same homogenous goods using a linear production
technology: the production of x units of output, requires x units of labor and
generates x units of environmentally damaging emissions. The production
costs are given by:
c(x) = wx + c x x 2 , (1)
where x is the output, w>0 the fixed wage rate, and c x > 0 a parameter for
simplicity sake, the demand is assumed infinitely elastic at the given price
˜p >w. Let p := ˜p − w>0. At each point of time, each firm can spend
an additional amount of money γ in order to reduce its current emissions
x. The investment
γ(v) = 1 2 v2 (2)
is needed, in order to reduce the firm’s emissions from x to max [x − v, 0].
The investment in one period has no impact on the emissions in future

Cheap-talk Multiple Equilibria and Pareto 105
period. Rather than expenditures in emission-reducing capital, γ can therefore
be interpreted as the additional costs resulting of a temporary switch
to a cleaner resource — for e.g., of a switch from coal to natural gas.
The firms attempts to maximize their profit. As we shall see at a later
place, one can assume without loss of generality that they disregard the
future and maximize in every τ, their current instantaneous profit. However,
the actual tax rate t enters their instantaneous profit function and is unknown
at the time when they choose v. Thus, they need to base their optimal
choice of v on an expectation (or, prediction) t e of t. In reality, a firm
can invest larger or smaller amounts of money in order to make or less
accurate predictions of the tax, the government will actually implement.
In this model, we assume for simplicity that each firm has two (extreme)
options for predicting the implemented tax. It can either suppose that R’s
announcement is truthful, that is, that t will be equal to t a , or it can do costly
research and try to better predict the t that will actually be implemented.
Depending upon the expectation-formation mechanism the firm chooses,
we speak of believer B or of a non-believer NB:
A believer considers the regulator’s announcement to be truthful
and sets
t e = t a (3)
This does not cost anything.
A non-believer makes a “rational” prediction of t, considering the current
number of Bs and NBs as constant. Making the prediction in any given
period τ costs δ>0.
Details on the derivation of the NBs’prediction will be given later. Note
that a firm can change its choice of expectation-formation mechanism at
any moment in time. That is, a B can become a NB, and vice versa. We
denote with π = π(t) ∈ [0, 1] the current fraction of Bs in the population.
Thus, 1 − π is the current fraction of NBs.
2.2. The Regulator, R
The regulator’s goal is to maximize with respect to t a ≥ 0 and t ≥ 0, the
inter-temporal social welfare function.
(t a ,t)=
∫ ∞
0
e −ρτ ϕ(t a ,t)dτ

106 Chirstophe Deissenberg and Pavel Ševčík
with
ϕ(t a ,t)= (πx B + (1 − π)x NB ) + πg B + (1 − π)g NB
− (π(x B − v B ) + (1 − π)(x NB − v NB )) 2
+ t(π(x B − v B ) + (1 − π)(x NB − v NB )), (4)
where x B ,x NB ,v B ,v NB denote the production respectively, investment
chosen by the believers B and the non-believers NB, and where g B (.)
and g NB (.) are their instantaneous profits,
g B = px B − c x (x B ) 2 − t(x B − v B ) − 1 2 (vB ) 2
g NB = px NB − c x (x NB ) 2 − t(x NB − v NB ) − 1 2 (vNB ) 2 − δ.
The strictly positive parameter ρ is a social discount factor.
Thus, the instantaneous welfare φ is the sum of: (1) the economy’s
output, that is also, the level of employment (remember that output and
employment are one-to-one in this economy); (2) the total profits of Bs
and NBs; (3) the squared volume of emissions and (4) the tax revenue. This
function can be recognized as a reasonable approximation of the economy’s
social surplus. The difference between the results of Dawid et al. (2005) and
those of the present article stem directly from the different specification of
the regulator’s objective function. In the former article, this function does
not include the firm’s profit and is linear in the emissions.
2.3. Dynamics
The firms switch between the two possible expectation-formation mechanisms
(B or NB), according to a imitation-type dynamics, see Dawid (1999);
Hofbauer and Sigmund (1998). Specifically, at each τ the firms meet randomly
two-by-two, each pairing being equiprobable. At every encounter,
the firm with the lower current profit adopts the belief of the other firm with
a probability proportional to the current difference between the individual
profits. Thus, on the average, the firms tend to adopt the type of prediction,
N or NB, which may currently leads to the highest profits. Above
mechanism gives rise to the dynamics.
dπ
=˙π = βπ(1 − π)g B − g NB . (6)
dt
Notice that ˙π reaches its maximum for π =
2 1 (the value or π for
which the probability, for encounter between firms with different profits are
(5)

Cheap-talk Multiple Equilibria and Pareto 107
maximized), and tends towards 0, for π → 0 and π → 1 (for extreme values
of π, all but very few firms have the same profits). The parameter β ≥ 0,
that captures the probability with which a firm changes its strategy during
one of these meetings, calibrates the speed of the information flow between
Bs and NBs. It can be interpreted as a measure of the firms’ willingness to
change strategies, that is, of the flexibility of the firms.
Equation (6) implies that by choosing the value of (t a ,t)at time τ the
regulator not only influences the instantaneous social welfare, but also the
future proportion of Bs in the economy. This, in turn, has an impact on
the future social welfare. Hence, there are no explicit dynamics for the
economy. This again has an impact on the future social welfare. Hence,
although there are no explicit dynamics for the economic variables v and
x, R faces a non-trivial inter-temporal optimization problem.
On the other hand, since the firms are atomistic, each single producer
is too small to influence the dynamics Eq. (6) of π, the only source of
dynamics in the model. Thus, the single firm does not take into account
any inter-temporal effect and, independently of its true planing horizon,
maximizes its current profit in every τ. This naturally leads us to examine
the (Nash) solution of the game between the regulator and the non-believers
that follows from the sequence (S) when, for an arbitrary, fixed value of π,
(a) R maximizes the integrand φ in Eq. (4) with respect to t a and t and (b)
the NBs maximize their profits with respect to ν NB and x NB . As previously
mentioned, we assume full information. In particular, the R and the NBs
are fully aware of the (non-strategic) behavior of the NBs.
The analysis of the static case is also necessary since, as previously
mentioned, it provides the prediction t e of the NBs.
3. The Sequential Nash Game
The game is solved by backwards induction, taking into account the fact
that the firms, being atomistic, rightly assume that their individual actions
do not affect the aggregate values, that is consider these values as given. We
consider only symmetric solutions where all Bs respectively, NBs choose
the same values for v and x.
3.1. Derivation of the Solution
The last decision in the sequence (S) is the choice of the production level x
by the firms. This choice is made after v and t are known. The firms being

108 Chirstophe Deissenberg and Pavel Ševčík
takers, the optimal symmetric production decision is:
x B = x NB = x = p − t
2c x
. (7)
Note that the optimal production is the same for Bs and NBs, as it
exclusively depends upon the realized taxes t.
In the previous stage, R chooses t given v B . Maximizing v NB with
respect to t, with x is given by (7) gives the optimal reaction function:
t(v B ,v NB ) = p − c x[2(πv B + (1 − π)v NB ) + 1]
1 + c x
. (8)
When the firms determine their investment v, Eqs. (7) and (8), and t a
are known, but the actual tax rate t is not. Using Eq. (7) in Eq. (5), one
recognizes that the firms choose v in order to maximize
That is, they set:
(p − t e 2
)
+ t e v − 1 4c x 2 v2 . (9)
v = t e (10)
The Bs predict that t will be equal to its announced value, t e = t a . Thus,
v B = t a . (11)
The NBs know that the regulator will act according to Eq. (8). Thus, they
choose:
v NB = p − c x[2(πv B + (1 − π)v NB ) + 1]
1 + c x
. (12)
Solving this last equation for v NB gives for the equilibrium value:
v NB = v NB (t a ) p − c x(1 + 2πt a )
1 + c x (3 − 2π) . (13)
The first decision to be taken is the choice of t a by R. The regulator’s
instantaneous objective function φ, using the results from the previous
stages, i.e., Eq. (7) for x, Eq. (11) for v B and Eq. (13) for v NB , is concave

with respect to t a for all π ∈ [0, 1], if,
Cheap-talk Multiple Equilibria and Pareto 109
c x > 1/ √ 3. (14)
We shall assume in the following that this inequality holds. Then, the
regulator will choose
t a$ =
1 + p . (15)
1 + 3c x
Using this last equation in Eq. (8) with v NB given by Eq. (13), one obtains
for the equilibrium value of t
t $ =
1 + p 1 + c x
−
1 + 3c x c x (3 − 2π) + 1 . (16)
Both t a$ and t $ will be non-negative if
which we assume from now on.
p ≥
3.2. Some Properties of the Solution
3
3c x − 2 , (17)
For all c x > 0 and π ∈ [0, 1], the optimal announcement t a$ is a constant,
and always less than t a$ . It is optimal to announce a high tax in order to
elicit a high investment from the believers, and to implement a low tax to
motivate a high production level. Moreover, t $ decreases in π: When the
proportion of Bs augments, the announcement t a becomes a more powerful
instrument making a recourse to t less necessary.
The difference between the statically optimal (i.e., evaluated at t $ ) profits
of NBs and Bs
g NB$ − g B$ = (1 + c x) 2
− δ, (18)
2c x (2π − 3) 2
is likewise increasing in π. Modulo δ, the profit of the NBs is always higher
than the profit of the Bs whenever π>0, reflecting the fact that the latter
make a systematic error about the true value of t. The profit of the Bs,
however, can exceed the one of the NBs if the prediction costs δ are high
enough.
Since t a$ is constant and t $ decreasing in π and since t $ ≤ t a$ , the
difference t a$ − t $ , increases with π. Therefore, the difference Eq. (18)
between the profits of the NBs and Bs is also increasing in the difference
between the announced and the implemented tax, t a$ − t $ ,

110 Chirstophe Deissenberg and Pavel Ševčík
Figure 1. The profits of the Bs (lower curve), of the NBs (middle curve), and the
regulator’s utility (upper curve) as a function of π for δ = 0.00025, c x = 0.6, p = 2.
As one would intuitively expect, the regulator’s instantaneous utility φ
too, increases with π. Most remarkable, however, is the fact that the profits of
both the Bs and NBs are also increasing in π (see Fig. 1 for an illustration).
An intuitive explanation is the following: For π = 0 the outcome is the
Nash solution of a game between the NBs and the regulator. This outcome
is not efficient leaving room for Pareto-improvement. As π increases, the
problem tends towards the solution a standard optimization situation with
the regulator as the sole decision-maker. This solution is efficient in the sense
that it does maximize the regulator’s objective function under the given
constraints. Since the objectives of the regulator are not extremely different
of the objectives of the firm, moving from the inefficient game-theoretic
solution to the efficient control-theoretic solution one improves the position
of all actors. Specifically, as π increases, the Bs enjoy the benefits of a lower
t, while the investment remains fixed at t a$ . Likewise, the NBs benefit from
the decrease in t. And R also benefits, because a raising number of Bs
are led by R’s announcement to invest more than they would, otherwise
and, subsequently, to produce more, to make higher profits, and to pollute
subsequently, to produce more, to make higher profits, and to pollute less.
In dynamic settings, however, the impact of the tax announcements
on the π dynamics may incite the regulator to reduce the spread between
t and t a , and in particular to choose t a

Cheap-talk Multiple Equilibria and Pareto 111
a high proportion of Bs to a low one, since it has one more instrument
(namely, t a ) to influence the Bs than to regulate the NBs. A high spread
t a − t, however, implies that the profits of the Bs will be low compared
to those of the NBs. This, by Eq. (6), reduces the value of ˙π and leads
over time to a lower proportion of Bs, diminishing the instantaneous utility
of R. Therefore, in the dynamic problem, R will have to find an optimal
compromise between choosing a high value of t a , which allows a low value
of t and insures the regulator a high instantaneous utility, and choosing a
lower one, leading to a more favorable proportion of Bs in the future. We
are going to explore these mechanisms in more details in the next section.
4. The Dynamic Optimization Problem
4.1. Formulation
Being atomistic, the firms do not recognize that their individual decisions
to choose the B or NB prediction technology influence π over time. Assume
that they consider π as constant. The regulator’s optimization problem is
then:
max (t a ,t) 0 ≤ t a (τ), t(τ)
(19)
such that Eqs.(6), (7), (11), (13), and π 0 = π(0).
Using
g := p − c x(1 + 2πt a )
1 + c x (3 − 2π) ,
h := p − t
(20)
.
2c x
The Hamiltonian of the above problem is given by
H(t a ,t,π,λ)= h + π
[h −
(p − t)2
4c x
+ t(h − t a ) − ta2
2
(p − t)2
+ (1 − π)
[h − + t(h − g) − 1 4c x
2 g2 − δ
+ t[π(h − t a ) + (1 − π)(h − g)]
− [π(h − t a ) + (1 − π)(h − g)] 2
+ λπ(1 − π)β
[tt a − ta2
2 − th + 1 ]
2 h2 + δ ,
where λ is the co-state.
]
]

112 Chirstophe Deissenberg and Pavel Ševčík
The first order maximization condition with respect to t a and t yields
for the dynamically optimal values*
t a∗ = (p − c x) + [c x (3 − 2π) + 1](1 + c x ) 2
, (21)
(1 + 3c x )[βλ(1 − π) + K]
with
t ∗ = (p − c x) + 2c x (1 + c x )π[c x (βλ(1 + 3c x )(1 − π) + 1)]
(1 + 3c x )[βπ(1 − π) + K]
K = 1 − 6c 3 x β2 λ 2 (1 − π) 2 π + 2c x [2 + 2βλ(1 − π)π]
+ cx 2 [3 − 2π + βλ(1 − π)(3 − 2βλ(1 − π)π)]. (22)
According to Pontriagin’s maximum principle, an optimal solution
(π(τ), (λ)) has to satisfy the state dynamics (6), evaluated at (t a∗ ,t ∗ ) plus:
˙λ = ρλ − ∂H(ta∗ (π, λ), t ∗ (π, λ), π, λ)
(23)
∂π
0 = lim
τ→∞ e−ρτ λ(τ). (24)
Due to the highly non-linear structure of the optimization problem an
explicit derivation of the optimal (π(τ), λ(τ)) seems infeasible. Hence, we
used Mathematica r○ to carry out a numerical analysis of the canonical
system Eqs. (6)–(23) in order to shed light on the optimal solution.
4.2. Numerical Results
Depending upon the parameter values, the model can have either two stable
equilibria separated by a so-called Skiba point, or a unique stable equilibrium.We
discuss first the more interesting case of multiple equilibria, before
carrying a summary of sensitivity analysis and briefly addressing the question
of the bifurcations, leading to a situation with a situation with unique
equilibrium. Unless and otherwise specified, the results presented pertain
to the reference parameter configuration c x = 0.6, p = 2, δ = 0.00025 that
underlies Fig. 1, together with ρ = 1, 0.0015. These are robust, with respect
to sufficiently small parameter variations: The same qualitative insights
would be obtained for a compact set of alternative parameter configurations.
From the onset, let us stress the fundamental mechanism that underlies
most of the results. Ceteris paribus, R would like to face as many Bs as
possible, since dφ/dπ >0. If the prediction costs δ are sufficiently high,
the profit difference g NB$ − g B$ see Eq. (18), will be negative at the current

Cheap-talk Multiple Equilibria and Pareto 113
value of π. In this case, by Eq. (6), implementing the statically optimal
actions t a$ , t $ suffices (albeit not optimally so) to insure that π increases
locally. In fact, for δ sufficiently large, the thus controlled system will
globally converge to a situation where there are only believers, π = 1.
However, if δ is small, the regulator cannot implement the actions t a$ , t $
since in that case g NB

114 Chirstophe Deissenberg and Pavel Ševčík
Figure 2. Phase diagram of the canonical system, c x = 0.6, p = 2, δ = 0.00025,
β = 1, and ρ = 0.0015.
E U
Table 1. Profits, welfare, and taxes at E U
and E L , c x = 0.6, p = 2, δ = 0.0025, β = 1,
p = 0.0015.
g φ t a
t
E U 1 2.25 1.07 0.12
E L 0.98 2.18 N.A. 0.62
The Pareto-superiority of E U is illustrated in Table 1 (remember that at
the equilibrium g N = g NB ).
The situation captured in Fig. 2 (an unstable equilibrium surrounded
by two stable ones) implies the existence of a threshold such that it is
optimal for R to follow a policy leading in the long-run towards the stable
equilibrium E L = (0,λ L ), whenever the initial value π 0 of π is inferior to
the threshold value, π 0

Cheap-talk Multiple Equilibria and Pareto 115
Whenever π 0 π s lies in the following
fact: The “deviation costs” that the regulator will have to accept initially in
order to steer the system towards the more favorable E U are so high that the
net benefit of going to E U would be less than the one obtained by letting
the system optimally converge towards the inferior E L .
The above results suggest that the policy of an environmental regulator
maybe very different depending on the fraction of the population that trusts
it when it initiates a new policy. If the initial confidence is high, the costs of
building a large fraction of Bs are compensated in the long-run by accrued
benefits. However, if the regulator’s trustworthiness is low from the onset,
its interest is to exploit its initial credibility for making short-term gains,
although this ultimately leads to an inferior situation where nobody trusts
the regulator.
As already mentioned, the dynamics of the canonical system Eqs. (6)–
(23) at the unstable middle equilibrium E M form a spiral. Therefore, the
threshold value π s is typically close to, but distinct from π M (i.e., π M ̸= π s )
and the threshold takes the particularly challenging form of a Skiba point.
No local analytical expression exists that characterizes a Skiba point. Thus,
Skiba points must be computed numerically. This was not done in this paper.
For a reference article on thresholds and Skiba points in economic models,
see Deissenberg et al. (2004).
5. Sensitivity Analysis and Bifurcations Towards
a Unique Equilibrium
Numerical analyses show that an increase in the firms’ flexibility (i.e., an
increase in β) shifts the stable equilibrium E U to the right and the unstable

116 Chirstophe Deissenberg and Pavel Ševčík
equilibrium E M as well as the Skiba point π s to the left. In other words,
if the firms react quickly to profit differences, the regulator will follow a
policy that leads to the upper equilibrium E U even if the initial proportion
of Bs is small. Indeed, the high speed of reaction of the firms means that the
accumulated costs incurred by the regulator on the way to E U will be small
and easily compensated by the gains around and at E U . Moreover, R does
not have to make Bs much better off than NBs to insure a fast reaction. As a
result, for β large, the equilibrium E U is characterized by a large proportion
of Bs and thus insures high stationary gains to all actors.
Not surprisingly, an increase of the discount factor ρ has the opposite
effect. Impatient regulators want to build up confidence, only if the initial
proportion of Bs is high. The resulting equilibrium value π U will be relatively
low, since the time and efforts needed now for an additional increase
in the stock of Bs weighs heavily compared to the expected future benefits.
An increase of the prediction cost δ finally, shifts E M to the left and
E U to the right: It is easier for R to incite the firms to use the B strategy,
favoring the convergence to equilibrium with a large number of believers.
The scenario with two stable equilibria separated by a Skiba point can
change qualitatively, when the parameter values are sufficiently altered.
For small values of β and/or δ and/or for large values of ρ, the equilibrium
E U collides with E M and disappears. Only one (stable) equilibrium
remains, E L . Thus, in the long-run, the proportion of believers tends to zero.
On the other hand, for large values of δ trying to outguess the regulator is
never optimal. The only remaining equilibrium is the one where everybody
is a believer.
6. Conclusion
The starting point of this paper is a static situation, where standard rational
behavior by all agents leads to a Pareto-inferior outcome, although
there is no fundamental conflict of interest either among the different firms
or between the firms and the regulator, and although the firms are perfectly
informed and perfectly predict the regulator’s actions. In addition
to the environmental problem studied here, such a situation is common for
instance in monetary economics, in disaster relief, patent protection, capital
levies, or default on debt.
The present paper and previous work strongly suggest that, in such a
situation, the existence of believers who take the announcements of a macroeconomic
regulator at face value typically, Pareto-improve the economic

Cheap-talk Multiple Equilibria and Pareto 117
outcome. This property hinges crucially on the fact that the private sector
is atomistic, and thus, that the single agents do not anticipate the collative
impact of their individual decisions. Moreover, it requires a relatively
benevolent regulator, whose objective function does not differ too drastically
from the one of the private agents.
To introduce dynamics, we assumed that the proportion of believers
and non-believers in the economy changes over time as a function of the
difference in profits for the two types of firms. The change obeys a word-ofmouth
process driven by the relative success of the one or the other private
strategy, to believe or to predict. It is supposed that the regulator recognizes
its ability to influence the word-of-month dynamics, by an appropriate
choice of actions and is interested not only in its instantaneous but also
in its future losses. It is shown that, when the firms react fast enough to the
difference in profits of Bs and NBs, a sufficiently patient regulator may use
incorrect announcements to Pareto-improve the economic outcome compared
to the situation where all firms are non-believers that perfectly predict
the regulator’s actions. A particularly interesting case arise, when a stable
Pareto-superior equilibrium with a positive fraction of believers co-exists
with the (likewise stable) perfect prediction but inferior equilibrium where
all firms are non-believers.
In this case, the optimal policy of the regulator (to converge towards
the one or the other equilibrium) depends upon the initial proportion of
believers in the population. This history dependence of the solution suggests
a promising meta-analysis of the importance of good reputation based on the
previous good governance, in situations where the same macro-economic
policy-maker is confronted with recurrent, distinct decision-making issues.
These results of this paper are obtained under the assumption that the
non-believers do not exploit the fact that the regulator announced tax differs
from the equilibrium announcement for the static game. Likewise, in the
model, the non-believers do not attempt to predict the dynamics of the number
of believers.We leave to future research, the non-trivial task of exploring
the consequences of a relaxation, of these two restrictive hypotheses.
References
Abrego, L and C Perroni (1999). Investment subsidies and time-consistent environmental
policy. Discussion Paper, Coventry: University of Warwick, 1–35.
Barro, R and D Gordon (1983). Rules, discretion and reputation in a model of monetary
policy. Journal of Monetary Economics 12, 101–122.

118 Chirstophe Deissenberg and Pavel Ševčík
Batabyal, A (1996a). Consistency and optimality in a dynamic game of pollution control I:
competition. Environmental and Resource Economics 8, 205–220.
Batabyal, A (1996b). Consistency and optimality in a dynamic game of pollution control II:
monopoly. Environmental and Resource Economics 8, 315–330.
Dawid, H (1999). On the dynamics of word of mouth learning with and without anticipations.
Annals of Operations Research 89, 273–295.
Dawid, H and C Deissenberg (2005). On the efficiency-effects of private (dis)-trust in the
government. Journal of Economic Behavior and Organization 57, 530–550.
Dawid, H, C Deissenberg and P Ševčík (2005). Cheap talk, gullibility and welfare in an
environmental taxation game. In: Dynamic Games: Theory and Applications, A Haurie
and G Zaccour (eds.), Amsterdam: Kluwer, 175–192.
Deissenberg, C and F Alvarez Gonzalez (2002). Pareto-improving cheating in a monetary
policy game. Journal of Economic Dynamics and Control 26, 1457–1479.
Deissenberg, C, G Feichtinger, W Semmler and F Wirl (2004). Multiple equilibria, history
dependence, and global dynamics in intertemporal optimization models. In Economic
Complexity: Non-Linear Dynamics, Multi-agents Economies, and Learning,
W Barnett, C Deissenberg and G Feichtinger (eds.), ISETE, Vol. 14, Amsterdam:
Elsevier, 91–122.
Dijkstra, B (2002). Time consistency and investment incentives in environmental policy.
Discussion Paper 02/12.U.K.: School of Economics, University of Nottingham, 2–12.
Gersbach, H and A Glazer (1999). Markets and regulatory hold-up problems. Journal of
Environmental Economics and Management 37, 151–164.
Hofbauer, J and K Sigmund (1998). Evolutionary Games and Population Dynamics.
Cambridge: Cambridge University Press.
Kydland, F and E Prescott (1977). Rules rather than discretion: the inconsistency of optimal
plans. Journal of Political Economy 85, 473–491.
Marsiliani, L and T Renstrom (2000). Time inconsistency in environmental policy: tax
earmarking as a commitment solution. Economic Journal 110, C123–C138.
McCallum, B (1997). Critical issues concerning central bank independence. Journal of
Monetary Economics 39, 99–112.
Petrakis, E and A Xepapadeas (2003). Location decisions of a polluting firm and the time
consistency of environmental policy. Resource and Energy Economics 25, 197–214.
Simaan, M and JB Cruz (1973a). On the Stackelberg strategy in nonzero-sum games. Journal
of Optimization Theory and Applications 11, 533–555.
Simaan, M and JB Cruz (1973b). Additional aspects of the Stackelberg strategy in nonzerosum
games. Journal of Optimization Theory and Applications 11, 613–626.
Vallee, T (1998). Comparison of different Stackelberg solutions in a deterministic
dynamic pollution control problem. Discussion Paper, LEN-C3E. France: University of
Nantes, 1–30.
Vallee, T, C Deissenberg and T Basar (1999). Optimal open loop cheating in dynamic
reversed linear-quadratic Stackelberg games. Annals of Operations Research 88,
247–266.

Chapter 4
Modeling Business Organization

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Topic 1
Enterprise Modeling and Integration:
Review and New Directions
Nikitas Spiros Koutsoukis
Hellenic Open University, and Democritus University
of Thrace, Greece
1. Introduction
Enterprise modeling (EM), Enterprise integration (EI), and Enterprise
integration modeling (EIM) are concerned with the definition, analysis,
re-design and integration of information, human capital, business process,
processing of data and knowledge, software applications and information
systems regarding the enterprise and its external environment to achieve
advancements in organization performance (Soon et al., 1997).
Enterprise modeling and Enterprise integration still are still ongoing
fields of research where the background and interests of contributors in
these areas are heterogeneous, including disciplines like mechanical manufacturing,
business process re-engineering, and software engineering.
However, the following two definitions (Vernadat, 1996) are representative
for current practices:
• Enterprise modeling is concerned with the explicit representation of
knowledge regarding the enterprise in terms models.
• Enterprise integration consists of breaking down organizational barriers
to improve synergy within the enterprise so that business goals are
achieved in a more productive way.
The main objective of this paper is to review the literature on EM and integration
and to provide a concise description of related topics. The paper also
discusses EM and integration challenges, and rationale as well as current
tools and methodologies for deeper analysis.
121

122 Nikitas Spiros Koutsoukis
2. Model and Enterprise Terminology
Model and enterprise are the two key terms that appear throughout this
paper. An enterprise can be perceived as “a set of concurrent processes executed
on the enterprise means (resources or functional entities) according
to the enterprise objectives and subject to business or external constraints”
(Vernadat, 1996). A model can be defined as “a structure that a system
can use to simulate or anticipate the behaviour of something else” (Hoyte,
1992). This is a generalization of a definition given by Minsky (1968):
“a model is a useful representation of some subject. It is a (more or less
formal) abstraction of a reality (or universe of discourse) expressed in terms
of some formalism (or language) defined by modeling constructs for the
purpose of the user”.
Instead of attempting to form a definition, which may be redundant, we
will mention some important features of enterprise models instead.
• An enterprise model provides a computational representation of the
structure, activities, processes, information, resources, people, behavior,
goals, and constraints of a business, government, or other enterprise.
It can be both descriptive and definitional-spanning what is and what
should be. The role of an enterprise model is to achieve model-driven
enterprise design, analysis, and operation (Fox, 1993).
• Enterprise models must either be represented in the mind of human beings
or in computers (Christensen et al., 1995).
• All enterprise models are built with a particular purpose in mind. Depending
on the purpose, the model will emphasize different types of information
at different levels of detail.
3. Enterprise Modeling
During the last decades, EM has been partly addressed by several
approaches to the same problem of making the enterprise more efficient.All
these approaches have included the construction of symbolic representations
of aspects of the real world, using various notations and techniques that
commonly could be denoted “conceptual modeling” (Solvberg and Kung,
1993). The idea of EM, as an extension of the standard for the exchange
of product model data (STEP) product modeling approach, contributes to
integrating design (which focuses on product information) and construction
(focusing on activity and resource information) (Kemmerer, 1999).

Enterprise Modeling and Integration 123
In the 1980s and during the early 1990s, when database technology was
applied on a larger scale, the need for better application design and development
methods became evident (Martin, 1982; Sager, 1988). Different
modeling methodologies, like the structured analysis and design technique
(SADT), were developed. A narrow focus on a single department or task
during development often caused operational problems across application
boundaries. The need for making more complete models aroused, integrating
operations across departmental or functional boundaries.
The problem in EM regarding the manufacturing of EI and control was
to ensure timely execution of business processes on the functional entities
of the enterprise (i.e., human and technical agents) to process enterprise
objects. Processes are made of functional operations and functional operations
are executed by functional entities. Objects flowing through the enterprise
can be information entities (data) as well as material objects (parts,
products, tools, etc.) (Rumbaugh, 1993).
In order to design the flexible information and communication
infrastructure needed, different enterprise models are useful, and the model
may in fact become a part of the integrated enterprise itself. The trend
now is away from the first single perspective enterprise models, which was
only focusing on the product data information handling, to more complete
enterprise models covering both informational and human aspects of the
organization (Fox, 1993).
During the 1990s, the question aroused on how to integrate different
departments in an enterprise, and how to connect the enterprise with its
external environment i.e., suppliers and customers, to improve co-operation
and logistics. During the 1990s, conglomerate industries took a more developmental
approach, and the research area of EI emerged. Enterprise modeling
is clearly a pre-requisite for EI as all things to be integrated and
coordinated need to modeled to some extent (Petrie, 1992).
Since 1990, major R&D programs for computer-integrated manufacturing
(CIM) have resulted in the following tools/methods or architectures
for EM:
(1) IDEF modeling tools: These are complementary modeling tools developed
by the integrated computer aided manufacturing (ICAM) project,
introducing IDEF0 for functional modeling, IDEF1 for information
modeling, IDEF2 for simulation modeling, IDEF3 for business process
modeling, IDEF4 for object modeling, and IDEF5 for ontology
modeling. IDEF models are mainly used for requirements definitions.
(2) Generic Artificial Intelligence (GRAI) integrated methodology: It is a
methodology which uses the GRAI grid, GRAI nets, developed by the

124 Nikitas Spiros Koutsoukis
GRAI laboratories of France and includes modeling IDEF0, and group
technology to model the decision making processes of the enterprise.
The combination is called GRAI integrated methodology (GIM).
(3) Computer integrated manufacturing open system architecture
(CIM-OSA): CIMOSA has been developed to assist enterprises adapt to
internal and external environmental changes so as to face global competition
and improve themselves regarding product prices, product quality,
and product delivery time. It provides four different types of views
of the enterprise: modeling function view, information view, resource
view, and organization view (Beeckman 1993; Vernadat, 1996).
(4) Purdue enterprise reference architecture (PERA): It is a methodology
developed at Purdue University in 1989 which focuses on separating
the human-based functions of an enterprise from the manufacturing
and information functions (Williams, 1994).
(5) Generalized enterprise reference architecture and methodology
(GERAM): It is a generalization of CIMOSA, GIM, and PERA. The
general concepts, identified and defined in this reference methodology,
consist of methodological guidelines for enterprise engineering (from
PERA and GIM), life-cycle guidelines (from PERA), and model views
modeling (e.g., CIMOSA constructs).
Modeling method relies upon a specific purpose defining its finality, i.e.,
the goal of the modeler. This finality has a direct influence on the definition
of modeling method. We adopt the position that any enterprise is made of a
large collection of concurrent business processes, executed by an open set
of functional entities (or agents) to achieve business objectives (as set by
management). Enterprise modeling and integration is essentially a matter
of modeling and integrating these process and agents (Kosanke and Nell,
1997; Ladet and Vernadat, 1995).
The prime goal of an EM approach is to support analysis of an enterprise
rather than to model the entire enterprise, even though this is theoretically
possible. In addition, another goal is to model relevant business process and
enterprise objects concerned with business integration.
According to Vernadat (1996), the aim of EM is to provide:
• a better perspective of the enterprise structure and operations;
• reference methods for enterprise engineering of existing or new parts of
the enterprise both in terms of analysis, simulation, and decision-making
and
• a model in order to manage efficiently the enterprise operations.

Whereas, the main motivations for EM are:
Enterprise Modeling and Integration 125
• better understanding of the structure and functions of the enterprise;
• managing complexity of operations;
• creating enterprise knowledge and know-how for all;
• efficient management of processes;
• enterprise engineering and
• EI itself.
4. Enterprise Integration
Enterprise integration was discussed since the early days of computers
in industry and especially in the manufacturing industry with CIM as the
acronym for operations integration (Vernadat, 1996). In spite of the different
understandings of the scope of integration in CIM, it was always understood
for information integration across or at least parts of the enterprise. Information
integration essentially consists of providing the right information,
to the right people, at the right place, at the right time (Norrie et al., 1995).
Information that is available to the right people, at the right place, at the
right time, and that enables them to act quickly and decisively, is a crucial
requirement of enterprises that intend to grow and remain profitable. The
intelligent delivery of information must obtain maturity levels consistent
with enterprise goals and must employ the appropriate technology to facilitate
this purpose. In today’s enterprise environment, users must consolidate
data and deliver it as useful information and knowledge that empowers the
right business decisions.
With this understanding the different needs in EI can be identified:
(1) Identify the right information to gain knowledge: Elicit knowledge from
gathering information from the intra-enterprise activities and use models
to represent this knowledge regarding product attributes and information,
process management issues, and the decision-making process.
(2) Provide the right information at the right place:The need for implementing
information sharing systems and integration platforms to support
information transaction across heterogeneous environments regarding
hardware, different operating systems, and the legacy systems. This
is a step towards inter-enterprise integration overcoming barriers and
provides connection between enterprise environments by linking their
operations to create extended and virtual enterprises.

126 Nikitas Spiros Koutsoukis
(3) Up-date the information in real time to reflect the actual state of the
enterprise operation: enterprises must be able to adopt changes regarding
both their external environment i.e., technology, legislation, and
their internal environment i.e., production operations in order to protect
the enterprise goal and objective from becoming obsolete.
(4) Co-ordinate business processes: This requires decisional capabilities
and know-how within the enterprise for real-time decision support
and evaluation of operational alternatives based on business process
modeling.
The aims of EI are:
• to enable communication among the various functional entities of the
enterprise;
• to provide interoperability of IT applications (plug-and-play approach)
and
• to facilitate coordination of functional entities for executing business
processes so that they synergistically fulfill enterprise goals.
The main motivation for EI is to make possible true interoperability
among heterogeneous, remotely located, systems within, or outside the
enterprise in an independent IT vendor environment.
Enterprise integration, especially for networked companies and large
manufacturing enterprises is becoming a reality. The issue is that EI is both
an organizational and a technological matter. The organizational matter
is partly understood so far whereas the technological matter lies with the
major advances over the last decade. It concerns mostly computer communications
technology, data exchange formats, distributed databases, object
technology, Internet, object request brokers (ORB such as OMG/CORBA),
distributed computing environments (such as OSF/DCE and MS DCOM,
and now Java to enterprise edition and execution environments (J2EE).
Some important projects developing integrating infrastructure (IIS)
technology for manufacturing environments include:
• CIMOSA IIS: The CIMOSA integrated infrastructure (IIS) enables
business process control in a heterogeneous IT environment. In IIS, an
enterprise is composed of functional entities, which are connected by a
communication system. Functional entities can be a machine, a software
application, or a human (Vernadat, 2002).
• AIT IP: This is an integration platform developed as an AIT project and
based on the CIMOSA IIS concepts (Waite, 1998).

Enterprise Modeling and Integration 127
• OPAL: This is also an AIT project that has proved that EI can be achieved
in design and manufacturing environments using existing ICT solutions
(Bueno, 1998).
• NIIIP (National industrial information infrastructure protocols) (Bolton
et al., 1997).
However, EI suffers from inherent complexity of the field, lack of established
standards, which sometimes happen after the fact, and the rapid and
unstable growth of the basic technology with a lack of commonly supported
global strategy. The EI modeling research community is growing at
a very rapid pace (Fox and Gruninger, 2003). The EIM research so far has
been mostly performed in large research organizations. A few pilot studies
have also been done in large organizations. Hunt (1991) suggests that EIM
is most beneficial to large industrial and government organizations. The
emphasis of current EIM research on large organizations is risky, and may
even have hampered the growth of the field. Enterprise wide modeling is
difficult in large organizations for two reasons: there is seldom any consensus
on exactly how the organization functions and the modeling task may
be so big that by the time any realistic model is built, the underlying domain
may have changed. Whatever these terms mean, we have to seek solutions
to solve industry problems, and this applies to EM and integration.
5. A Framework Setting for EI Modeling
Enterprise integration is a multifaceted task employed for addressing challenges
stemming from various aspects of the globalized economy. The contemporary
business world, economically, politically, and technologically is
a fast-changing world and most if not all enterprises, from small to large,
are continually challenged to evolve as rapidly as the world around them
evolves. Enterprise integration allows an enterprise to function coherently
as a whole and to shift its primary value chain activities in tandem with
its secondary value chain activities according to the challenges or requirements
posed by the enterprise environment or goals set by the enterprise
itself, and most frequently a combination of both (Giachetti, 2004). In this
context, the value chain’s primary and secondary activities are used simply
as a well-known functional-economic view of the enterprise in order to
communicate coherently, as opposed to a semantically accurate or complete
view of the enterprise (Porter, 1985).

128 Nikitas Spiros Koutsoukis
The multiple facets of EI refer to the multiple dimensions, entities, and
constituents where integration is primarily aimed at, and through which
enterprise integration is achieved.
Enterprise integration dimensions represent infrastructural views, upon
which integration is founded, built and subsequently achieved. Some of the
most commonly used integration dimensions are the following:
• the data and information dimension;
• the processes dimension;
• the economic activity or business dimension and
• the technology or technical dimension.
Because these dimensions can easily be extended throughout the enterprise
regardless of the enterprise functions, they are frequently used as
fundamental reference points for EI efforts (Lankhorst, 2005).
Each of these dimensions has been used successfully for seeking out and
achieving EI. For instance, in the data and information dimension, which
is mainly the realm of corporate information systems, data warehousing
and enterprise resource planning (ERP), have been used successfully to
introduce enterprise-wide, unified views of data, information and related
analyses. In the processes dimension, business process management (BPM)
or re-engineering (BPR) have been successfully applied in developing and
refining old, and new processes which are more integrated and efficient
across the enterprise. In the economic or business dimension, business
strategy models, like the core-competency theory, balanced-score cards,
or economic value-added models like the activity-based costing (ABC)
are also used successfully to integrate across the enterprise (Kaplan and
Norton, 1992; Prahalad and Hamel, 1990). In the technology or technical
dimension, the key requirement is for interoperability of systems, hardware,
and software. The success with which many multinational enterprises
operate shows that certain milestones have been reached in this
direction.
Enterprise entities refer to function-oriented enterprise constructs
that are typically goal-oriented, collectively contributing to achieving
the enterprise mission. Entities form hierarchical views of the enterprise,
and frequently tend to match formal or informal structures as in
most organizational charts. From a functional perspective, entities refer
to key organizational activities or divisions, such as administration, production,
accounting, sales, marketing, procurement, and R&D. As is well
known, entities can also be organized in terms of authority or delegation

Enterprise Modeling and Integration 129
layers, communication layers, goal-contribution layers, geographically
based activities and so forth.
The sole purpose for having such functional-oriented constructs is to
decompose the enterprise into smaller, more specific, and more manageable
parts. The contribution of each entity to the enterprise objectives is thus
readily identified and narrowed down in scope, horizontally or vertically.
It is only through the use of one or more dimensions that the entities are
re-combined in an enterprise-wide integration model.
Enterprise constituents or constituent groups refer to the human factor
which is ultimately responsible for setting out, applying and achieving EI.
The most prevalent constituent groups are the following:
• Stakeholders
• Decision-makers
• Employees
which are internal to the enterprise, and
• Suppliers and
• Clients
which are external to the enterprise.
Some of the main pitfalls in EI lie at the constituents’ level. This is
because the constituents are, in one way or another, autonomous or semiautonomous
agents acting primarily in their own interest, which is defined
mainly by their position in enterprise coordinates terms. We consider the
following fundamental dimensions as the main enterprise coordinates for
positioning the constituents:
• level of authority and
• immediacy of contribution to goals (from strategic to operational, abstract
to specific)
which can also be inverted to
• level of responsibility and
• level of activity (from strategic to operational, or abstract to specific)
The higher the level of authority, the more strategic or abstract are the
actions that the constituents take in enterprise terms. At this level, constituents
have a bird’s-eye view of the enterprise and find it easier to match
organizational outcomes to personal interest i.e., the bird’s-eye view makes
it easier to view the enterprise as a single entity. On the other hand, the

130 Nikitas Spiros Koutsoukis
lower the level of authority the more operational or specific the actions
that the constituents take in enterprise terms. At this level, constituents find
it harder to consider a single-entity view of the organization, and hence
organizational outcomes are less easily matched to personal interests.
It follows that inconsistencies in the constituents’ perspectives have the
ability to cancel out some of the main benefits that the other two facets bring
forward, namely the unified view of the enterprise as single entity and the
immediacy with which operational activities contribute to strategic goals.
Inconsistencies in constituents’ perspectives are being addressed mainly
through leadership and human resource practices, which aim to put in place
an organizational culture, or otherwise a unified perception of what the
enterprise stands for, its values and its practices among other things. Mission
statements, codes of practice, and team building exercises are some of the
most frequently used tools for scoping and setting out a unified, constituent
view of the enterprise.
Thus, a strong requirement is surfacing for developing new EI modeling
frameworks, which are able to incorporate heterogeneous modeling constructs,
such as the dimensions, entities or constituents considered above.
We find that some of the key requirements are set out as follows:
(a) Interchangeable dimensions: EI models should be able to shift between
the dimensions considered above, without loss of context.
(b) Use of hybrid modeling constructs: EI models should be able to utilize
interchangeably modeling constructs for representing any type of enterprise
activity unit, including procedural units, physical or logical units,
inputs or outputs, tangible and intangible processes, decision-making
points, etc.
(c) Ability to consolidate or analyze to successive levels of detail: this is
particularly useful for communicating enterprise structures throughout
multiple echelons and hierarchy levels. For instance, stakeholders will
most likely need access to a consolidated view of the integrated enterprise
whereas employees are most likely to require a position-centred
view of the enterprise, with detailed surroundings that are consolidated
further away from the employee’s position.
(d) Ability to interchange between declarative and goal-seeking states of
the integration models: when in declarative mode, models work simply
as formal structures, or simulators of how the integrated enterprise
operates. In goal-seeking mode, the model emphasizes improvements
that can lead to goal attainment or “satisfying,” to use Simon’s term
(Simon, 1957).

Enterprise Modeling and Integration 131
Of course, these requirements can be analyzed further and in detail, but
such a discussion would be beyond the scope of this paper. Still, we also
find that these requirements are suffice to set out an agenda for further work
in the domain of EI and EI modeling.
6. Discussion
At the current state of technology, we find that EM and integration are
becoming familiar within the large enterprises that seem to understand the
need of acquiring their concept. However, in accordance with Williams
(1994) we also find that the reason for the moderate success and rather not
so extended use of EM and integration initiatives include:
(a) Cost: It is commonly accepted that such efforts are very expensive and
it is rather difficult to argue on the benefits of the outcome from the
beginning of each project.
(b) Project size and duration: Indeed, such projects cannot be completed
but they require time. Quite a large number of people will be involved
and high levels of commitment on behalf of the enterprise are required.
(c) Complexity: EI is a never-ending process and parameters such as the
legacy systems within large enterprises resisting integration have to
be seriously considered. There is the need for a global vision with a
modular implementation approach.
(d) Management support: Management facing high cost may resent to support
such projects. It is very important that management be part of the
project and be fully committed to it.
(e) Skilled people: The human factor concerning high-skilled employees
involved in the projects is vital for success. Unfortunately, due to limited
training schemes experienced users are scarce.
Nevertheless, the enthusiasm of the research community and the industry
remains intact trying to overcome problems and difficulties by creating
tools and adopting methodology that will make a difference. Nowadays,
EM and integration mostly rely upon advanced computer networks, the
worldwide web and Internet, integration platforms as well as ERPs, and
data exchange formats (Chen and Vernadat, 2002; Martin et al., 2004).
A big issue is that both EM and EI are nearly totally ignored by SME’s
and there is still a long way to go before SME’s will master these techniques
on their own and in this case, they have to quickly catch on the technology
and define which tools they have to use.

132 Nikitas Spiros Koutsoukis
Some researchers like Vernadat, Kosanke, Tolone, and Zeigler consider
that this technology would better penetrate and serve any kind of
enterprises if:
• They identify users and a specific EIM problem. An example of an EIM
problem is how to produce high-quality products at low cost.
• They make a prototype EIM that addresses the problem, contributing in
the decision-making process based on a simple initial model accepted by
the majority of the users (Tolone et al., 2002).
• There was a standard vision on what EM really depend and there was an
international consensus on the underlying concept for the benefit of the
business users (Kosanke et al., 2000).
• There was a standard, user-oriented, interface in the form of a unified
enterprise modeling language (UEML) based on the previous consensus
to be available on all commercial modeling tools.
• There were real EM and simulation tools commercially available in the
market place taking into account function, information, resource, organization,
and financial aspects of an enterprise including human aspects,
exception handling, and process coordination. Simulation tools need to
be configurable, distributed, and agent-based simulation tools (Vernadat
and Zeigler, 2000).
However, it is rather unlikely that a single EIM that will be equally
applicable to all organizations. Each organization will have to develop its
own strategy and philosophy (Fox and Huang, 2005). Despite the different
approaches (frameworks) of EIM, we always have to bear in mind the
following functional requirements of an EIM framework (Patankar and
Adiga, 1995):
(1) Decision orientation. An EI model based on any particular concept of
an EM framework should support the decision-making process considering
thoroughly all factors of the external and internal environment
affecting the enterprise.
(2) Completeness. EM frameworks should be able to represent all aspects
of the enterprise such as business units, business data, information
systems, and external partners i.e., suppliers, sub-contractors, and
customers.
(3) Appropriateness. EIM frameworks should be representing the enterprise
at appropriate levels by providing models that can be understood
by people with heterogeneous backgrounds.

Enterprise Modeling and Integration 133
(4) Permanence. The EI model should remain consistent with the enterprise’s
overall objectives even when the enterprise is in the process of
changing due to management changes or other. Models should remain
true and valid within the enterprise.
Finally, the EIM frameworks should be simply structured, flexible,
modular, and generic to ensure that the framework is applicable across different
manufacturing operations and enterprises. In addition, the framework
should relate to both manual and automatic processes. This will provide the
basis for proper and complete integration.
Modeling and integration always mean effort in time and costs.
Nevertheless, to handle complexity in business environments we see the
above-mentioned elements moving from “luxury articles” to “everyday
necessities”.
These are some of the challenges to be solved in future to build extended
interoperable manufacturing enterprises as there is unlikely to be a single
EIM methodology, which will be equally applicable to all organizations
(Li and Williams, 2004). Each organization will have to develop its own
strategy and philosophy. However, EIM promises to be a revolutionary
technology.
Finally, the success of EI efforts lies in the ability to iron out incoherencies
and lack coordination between the multiple facets considered above.
This is a complex and challenging task, and lies at the heart for EI modeling.
Many of the multiple modeling frameworks considered above, like
IDEF, CIM-OSA, or GERAM for example, have stemmed from integration
efforts in the areas of manufacturing or engineering, and while successful
in their own right, these frameworks are still lagging behind when it comes
to integrating across the multiple dimensions, entities and constituents of a
contemporary enterprise that we have identified above.
7. Epilogue
This paper has provided a description of the main issues on EM and EI.
It has become quite evident from the literature that both the issues are complex
and require knowledge on various disciplines particularly on organizational
management, engineering, and computer science. As such, it can be
generalized that EM and integration mainly revolves around organizational
modeling from which the analysis, design, implementation and integration
of the organization management, business processes, software applications,
and physical computer systems within an enterprise are supported.

134 Nikitas Spiros Koutsoukis
We believe that although we are rich in technology to solve isolated
business problems (e.g., product scheduling, quality control, production
planning, accounting, marketing, etc.), many other problems still reside
within the enterprise. Solving these problems require an integrated approach
to problem solving. This integration must start at the representation level
and the entire enterprise together with its structure, functionality, goals,
objectives, constraints, people, processes, products must be modeled. The
solution will probably be the outcome of an EIM framework.
References
Beeckman, D (1993). CIM-OSA: computer integrated manufacturing open system architecture.
International Journal of Computer Integrated Manufacturing 2(2), 94–105.
Bolton, R, A Dewey, A Goldschmidt and P Horstmann (1997). NIIIP — the national industrial
information infrastructure protocols. In Enterprise Engineering and Integration:
Building International Consensus, K Kosanke and JG Nell (eds.), Berlin: Springer-
Verlag. pp. 293–306.
Bueno, R (1998). Integrated information and process management in manufacturing engineering.
Proc. of the 9th IFAC Symposium on Information Control in Manufacturing
(INCOM’98), pp. 109–112. France: Nancy-Metz, May 24–26.
Chen, D and FVernadat (2002). Enterprise interoperability: a standardisation view. ICEIMT
2002, 273–282.
Christensen, LC, BW Johansen, N Midjo, J Onarheim, TG Syvertsen and T Totland (1995).
Enterprise Modeling-Practices and Perspectives. In Proc. of 9th ASME Engineering
Database Symposium, Rangan (ed.), Boston: Massachusetts, 1171–1181.
Fox, MS (1993). Issues in Enterprise Modeling. Proc. of the IEEE Conference on Systems.
Man and Cybernetics, France: Le Touquet, 83–98.
Fox, MS and M Gruninger (2003). The logic of enterprise modeling, modeling and methodologies
for enterprise integration. In Modelling and Methodologies of Enterprise
Integration, P Bernus and L Nemes (eds.), Cornwall, Great Britain: Chapman and
Hall, 83–98.
Fox, MS and J Huang (2005). Knowledge provenance in enterprise information.
International Journal of Production Research 43(20), 4471–4492.
Giachetti, RE (2004). A framework to review the information integration of the enterprise.
International Journal of Production Research 42(6), 1147–1166.
Hoyte, J (1992). Digital models in engineering — a study on why and how engineers build
and operate digital models for decision support. PHD Thesis, University of Trondheim,
Norway.
Hunt, DV (1991). The Integration of CALS, CE, TQM, PDES, RAMP, and CIM, Enterprise
Integration Sourcebook. San Diego, CA: Academic Press.
Kaplan, RS and DP Norton (1992). The balanced scorecard: measures that drive
performance. Harvard Business Review 70(1), 71–79.
Kemmerer, J (1999). STEP: The Grand Experience, NIST Special Publication SP939,
Washington, C 20402, USA: US Government Printing Office.
Kosanke, K and JG NelI (1997). Enterprise Engineering and Integration: Building
International Consensus. Berlin: Springer-Verlag.

Enterprise Modeling and Integration 135
Kosanke, K, F Vernadat and M Zelm (2000). Enterprise engineering and integration in the
global environment. Advanced Network Enterprises 2000, Berlin, 61–70.
Ladet, P and FB Vernadat (1995). Integrated Manufacturing Systems Engineering. London:
Chapman & Hall.
Lankhorst, M (2005). Enterprise Architecture at Work. Berlin: Springer-Verlag.
Li, H and TJ Williams (2004). A Vision of Enterprise Integration Considerations. Toronto,
Canada: ICEIMT 2004.
Martin, J (1982). Strategic Data-Planning Methodologies. Englewood Cliffs, New York:
Prentice-Hall.
Martin, J, E Robertson and J Springer (2004). Architectural Principles for Enterprise Frameworks:
Guidance for Interoperability. Toronto, Canada: ICEIMT 2004.
Minsky, M (1968). Semantic Information Processing. Cambridge, MA: The MIT Press.
Norrie, M, M Wunderli, R Montau, U Leonhardt, W Schaad and HJ Schek (1995).
Coordination approaches for CIM. In Integrated Manufacturing Systems Engineering.
P Ladet and FB Vernadat (eds.), London: Chapman & Hall pp. 221–235.
Patankar, AK, and S Adiga (1995). Enterprise integration modeling: a review of theory and
practice. Computer Integrated manufacturing Systems 8(1), 21–34.
Petrie, CJ (1992). Enterprise Integration Modeling. Cambridge, MA: The MIT Press.
Porter, M (1985). Competitive Advantage. New York: Free Press.
Prahalad, CK and G Hamel (1990). The core competence of the organisation. Harvard
Business Review 68(3), 79–91.
Rumbaugh, J (1993). Objects in the constitution — enterprise modeling. Journal on Object
Oriented Programming, January issue, 18–24.
Sager, MT (1988). Data concerned enterprise modeling methodologies — a study of practice
and potential. The Australian Computer Journal 20(3), 59–67.
Simon, H (1957). Models of Man: Social and Rational. New York: Wiley.
Solvberg, A and DC Kung (1993). Information Systems Engineering — An Introduction.
New York: Springer-Verlag.
Soon, HL, J Neal and A Pennington (1997). Enterprise modeling and integration: taxonomy
of seven key aspects. Computers in Industry 34, 339–359.
Tolone, W, B Chu, G.-J Ahn, R Wilhelm and JE Sims (2002). Challenges to Multi-Enterprise
Integration. ICEIMT 2002, 205–216.
Vernadat, FB (1996). Enterprise Modeling and Integration: Principles and Applications.
London: Chapman & Hall.
Vernadat, F (2002). Enterprise modeling and integration. ICEIMT 2002, 25–33.
Vernadat, FB and BP Zeigler (2000). New simulation requirements for model-based Enterprise
Engineering. Proc. of IFAC/IEEE/INRIA Internal Conference on Manufacturing
Control and Production Logistics (MCPL’2000). Grenoble, 4–7 July 2000. CD-ROM.
Waite, EJ (1998). Advanced Information Technology for Design and Manufacture. In Enterprise
Engineering and Integration: Building International Consensus. K Kosanke and
JG Nell (eds.), Berlin: Springer-Verlag, pp. 256–264.
Williams, TJ (1994). The purdue enterprise reference architecture. Computers in Industry,
24(2–3), 141–158.

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Topic 2
Toward a Theory of Japanese Organizational
Culture and Corporate Performance
Victoria Miroshnik
University of Glasgow, UK
1. Introduction
Japanese national culture has a specific influence on the organizational
culture (OC) of the Japanese companies. In order to understand these aspects
of culture that are affecting corporate performance, a systematic analysis of
the national culture (NC) and OC is essential. The purpose of this chapter
is to provide a scheme to analyze this issue in a systematic way.
National culture can affect corporate OC (Aoki, 1990; Axel, 1995;
Hofstede, 1980) and corporate performance (CP) (Cameron and Quinn,
1999; Kotter and Heskett, 1992). Multinational corporations with its supposedly
common OC demonstrate different behaviors in different countries,
which can affect their performances (Barlett and Yoshihara, 1988; Calori
and Sarnin, 1991). National culture with its various manifestations can create
unique organizational values for a country, which in conjunction with
the human resources management (HRM) practice may create some unique
OC for a corporation. Organizational culture along with a leadership style,
which is the product of OC, NC, and HRM practices, creates a synergy,
which shapes the fortune of the company’s performances. Thus, NC, organizational
values, OCs, leadership styles, human resources practices, and
CPs are inter-related and each depend on the other. If a company maintains
this harmony it can perform well, otherwise it declines.
The structure of this chapter is as follows. In Section 2, relationship
between NCs, OC, and performances, as given in the existing literature, is
analyzed. In Section 3, the Japanese culture was analyzed along with the
controversies on this issue. In Section 4, the new approach of the nationorganization-performance
exchange model (NOPX) is explained in detail
and the theoretical propositions underlying this model are analyzed.
137

138 Victoria Miroshnik
2. Corporate Performance, the Highest Stage of National
and Organizational Culture: A Synthesis
Culture is multidimensional, comprising of several layers of inter-related
variables. As society and organizations are continuously evolving, there is
no theory of culture valid at all times and locations. The core values of a
society (macro-values (MAVs)) can be analyzed by asking the following
questions:
(a) What are the relationships between human and nature? (b) What are
the characteristics of innate human nature? (c) What is the focus regarding
time — whether past, future, or present, or a combination of all these?
(d) What are the modalities of human activity, whether spontaneous or
introspective or result-oriented or a combination of these? (e) What is the
basis of relationship between one man and another in the society?
In the structure of the NC, there are certain micro or individual values,
which include sense of belonging, excitement, fun and enjoyment,
warm relationship with others, self-fulfilment, being well-respected, and a
sense of accomplishment, security, and self-respect (Kahle, et al., 1988).
Although Hofstede (1990; 1993) has the opinion that the perceived practices
are the roots of the OC rather than values, most researchers have accepted
the importance of values in shaping cultures in several organizations.
Combinations of micro-values (MIVs) and macro-values (MAVs) can
give rise to an OC, given certain meso-values (MEV) or organizational
values, which are specific for a country. Meso-values are certain codes of
behavior, which influences the future, and the expected behavior of the
members of the society, if they want to belong to the main stream. These
vary from one society to another, as the expectations of different societies,
as products of historical experiences, religious, and moral values are
different.
Cultural values are shared ideas about what is good, desirable, and
justified; these are expressed in a variety of ways. Social order, respect for
traditions, security, and wisdom are important for the society, which is like
an extended family.
According to Schein (1997), OC emerges from some common assumptions
about the organization, which the members share as a result of their
experiences in that organization. These are reflected in their pattern of
behaviors, expressed values, and observed artefacts. Organizational culture
provides accepted solutions to known problems, which the members
learn and feel about and forms a set of shared philosophies, expectations,

Toward a Theory of Japanese Organizational Culture 139
norms, and behavior patterns, which promotes higher level of achievements
(Kilman et al., 1985; Marcoulides and Heck, 1993; Schein, 1997).
Organizational culture, for a large and geographically dispersed organization,
may have many different cultures. According to Kotter and Heskett
(1992), leaders create certain vision or philosophy and business strategy
for the company. A corporate culture emerges that reflects the vision and
strategy of the leaders and experiences they had while implementing these
strategies. However, the question is whether it is valid for every NC.
A combination of MAVs, MEVs, and MIVs creates a specific OC,
which varies from country to country according to their differences in
NC. Hofstede (1980; 1985; 1990; 1993) showed the relationship between
NC and OC. Global leadership and organizational behavior effectiveness
(GLOBE) research project has tried to identify the relationships among
leadership, social culture, and OC (House, 1999).
Cameron and Quinn (1999) have mentioned that the most important
competitive advantage of a company is its OC. If an organization
has a “strong culture” with “well-integrated and an effective” set of values,
beliefs, and behaviors, it normally demonstrates high level of CPs
(Ouchi, 1981).
Denison and Mishra (1995) have attempted to relate OC and performances
based on different characteristics of the OC. However, different
types of OC enhance different types of business (Kotter and Heskett, 1992).
There is no single cultural formula for long-run effectiveness. As Siehl and
Martin (1988) have observed, culture may serve as a filter for factors that
influence the performance of an organization. These factors are different for
different organizations. Thus, a thorough analysis regarding the relationship
between culture and performances is essential.
3. Japanese National and Organizational Culture
Japanese firms are considered to be of a family unit with long-term orientations
for HRM and with close ties with other like-minded firms,
banks, and the government. The OC promotes loyalty, harmony, hard
work, self-sacrifice, and consensus decision-making. These, along with
lifetime employment and seniority-based promotions, are considered to
be the natural outcome of the Japanese NC. (Ikeda, 1987; Imai, 1986;
Ouchi, 1981). Japanese workers’ psychological dependency on companies
emerges from their intimate dependent relationships with the society and the
nation.

140 Victoria Miroshnik
Japanese NC has certain MIVs: demonstration of appropriate attitudes
(taido); the way of thinking (kangaekata); and spirit (ishiki), which forms
the basic value system for the Japanese (Kobayashi, 1980). Certain MEVs
can be identified as the core of the cultural life for the Japanese, if they want
to belong to the mainstream Japanese society (Basu, 1999; Fujino, 1998).
These are (a) Senpai-Kohai system; (b) Conformity; (c) Hou-Ren-Sou and
(d) Kaizen or continuous improvements.
Senpai-Kohai or senior-junior relationships are formed from the level
of primary schools where junior students have followed the orders of the
senior students, who in turn, may help the juniors in learning. The process
continues throughout the lifetime for the Japanese. In work places, Senpais
will explain Kohais how to do their work, the basic code of conducts and
norms.
From this system emerges the second MEV, Conformity, which is better
understood from the saying that “nails that sticks out should be beaten
down”. The inner meaning is that unless someone conforms to the rules
of the community or co-workers, he/she would be an outcaste. There is no
room for individualism in the Japanese society or in work place.
The third item, Hou-Ren-Sou, is the basic feature of the Japanese
organizations. Hou-Ren-Sou, is a combination of three different words in
Japanese: Houkoku i.e., to report, Renraku i.e., to inform and Soudan i.e.,
to consult or pre-consult.
Subordinates should always report to the superior. Superiors and subordinates
share information. Consultations and pre-consultations are required;
no one can make his/her decision by himself/herself even within the delegated
authority. There is no space in which the delegation of authority may
function. Combining these words, Houkoku, Renraku, and Soudan, “Hou-
Ren-Sou” is the core value of the culture in Japan. Making suggestions, for
improvements, without pre-consultations is considered to be an offensive
behavior in Japanese culture. Everyone from the clerk to the president, from
the entry day of the working life to the date of retirement, every Japanese
must follow the “Hou-Ren-Sou” value system.
Kaizen i.e., continuous improvement is another MEV that is one of the
basic ingredients of the Japanese culture. Search for continuous improvement
during the Meiji Government of the 19th century led them to search the
world for knowledge. Japanese companies today are doing the same in terms
of both acquisitions of knowledge by setting up R&D centers throughout
the western world, and by having “quality circles” in work places in order to
implement new knowledge to improve the product quality and to increase
its efficiency (Kujawa, 1979; Kumagai, 1996; Miyajima, 1996).

Toward a Theory of Japanese Organizational Culture 141
3.1. Japanese OC
In order to understand the Japanese OC, it is essential to know the Japanese
system of management, which gave rise to the unique Japanese style of OC.
What is written below is the result of several visits to the major Japanese
corporations (like Toyota, Mitsubishi, Honda, and Nissan) and interviews
with several senior executives, including members of the board and vicepresidents
of these companies.
Japanese system of management is a complete philosophy of organization,
which can affect every part of the enterprise. There are three basic
ingredients: lean production system, total quality management (TQM) and
HRMs (Kobayashi, 1980). These three ingredients are inter-linked in order
to produce total effect on the management of the Japanese enterprises.
Because Japanese overseas affiliates are part of the family of the parent
company, their management systems are part of the management strategy
of the parent company (Basu, 1999; Morishima, 1996; Morita, 1992;
Shimada, 1993).
The basic idea of the lean production system and the fundamental
organizational principles is the “Human-ware” (Shimada, 1993), which is
described in Fig. 1. “Human-ware” is defined as the integration and interdependence
of machinery and human relations and a concept to differentiate
among different types of production systems. The purpose of the lean production
philosophy, which was developed at the Toyota Motor Company,
is to lower the costs. This is done through the elimination of waste —
everything that does not add value to the product. The constant strive for
perfection (Kaizen in Japanese) is the overriding concept behind good management,
in which the production system is being constantly improved;
perfection is the only goal. Involving everyone in the work of improvement
is often accomplished through quality circles. Lean production system uses
“autonomous defect control” (Pokayoke in Japanese), which is an inexpensive
means of conducting inspection for all units to ensure zero defects.
Quality assurance is the responsibility of everyone. Manufacturing tasks
are organized into teams. The principle of “just-in-time” (JIT) means, each
NC OC
LC CP
Where “NC” is “National Culture”; “OC” is “Organizational Culture”; “LC” is
“Leader Culture”; and, “CP” is “Corporate Performance”.
Figure 1.
Sub-model 1: culture-performance system.

142 Victoria Miroshnik
process should be provided with the right part, in the right quantity at exactly
the right point of time. The ultimate goal is that every process should be
provided with one part at a time, exactly when that part is needed.
The most important feature of the organizational set-up of the lean
production system is the extensive use of multifunctional teams, which
are groups of workers who are able to perform many different works. The
teams are organized along a cell-based production flow system. The number
of job-classifications also declines. Workers have received training to
perform a number of different tasks, such as the statistical process control,
quality instruments, computers, set-up performances, maintenance etc. In
the lean production system responsibilities are decentralized. There is no
supervisory level in the hierarchy. The multifunctional team is expected
to perform supervisory tasks. This is done through the rotations of team
leadership among workers. As a result, the number of hierarchical levels in
the organization can be reduced. The number of functional areas that are
the responsibility of the teams increases (Kumazawa and Yamada, 1989).
In a multifunctional set-up, it is vital to provide information in time
and continuously in the production flow. The production system is changing
and gradually adopting a more flexible system in order to adopt itself to
changes in demand; which may reduce costs of production and increase efficiency.
There are extensive usages of Kaizen activities and TQM and Total
Productive Maintenance (TPM) to increase the effectiveness of corporate
performances.
4. A Nation-Organization-Leader-Performance Model
Organizational culture is a product of a number of factors: NC, human
resources practice, and leadership styles have prominent influences on it.
These in turn, along with the OC, affect CPs. The proposed model, as in
Fig. 1, is the synthesis of the ideas relating to this central theme. Figures 2
and 3 describe the proposed theoretical model relating OC and CPs. Corporate
performances are measured in terms of the following criteria:
(a) customers’ satisfaction;
(b) employee’s satisfaction and commitment and
(c) contributions of the organization to the society and environment.
Most companies in Japan use these criteria to signify CPs (Basu, 1999;
Nakane, 1970).
There are several latent or hypothetical variables, which jointly can
influence the outcome. National culture is affected by two constructs:

Toward a Theory of Japanese Organizational Culture 143
MIVs and MAVs. Micro-values (MIVs) are composed of several factors
(Kahle et al., 1988). These are: (1) the sense of belonging; (2) respect
and recognition from others and (3) a sense of life accomplishments and
(4) self-respect.
Macro-values, according to the opinions of the executives of the
Japanese, firms are religious values, habitual values, and moral values.
There may be other MAVs, which are important for other nations like geography,
racial origin, etc., but for the Japanese, these are not so important
(Basu, 1999). Although moral and habitual values can be the results of
religious values, it is better to separate out these three values as distinct.
The moral and habitual values are different in Japan from other East Asian
nations. Honor and “respect from others” are central to the Japanese psychology.
Ritual suicides (Harakiri) are honorable acts for the Japanese, if
they fail in some way to do their duty. Habitual values are extreme politeness
on the surface, beautifications of everything, community spirit, and cleanness
are unique in Japan, which are not followed in any other countries
in Asia.
This is particularly true if we examine certain MEVs, which are neither
MIV nor MAV values, but are derived from the NC. It is possible to identify
five different MEVs, which are important outcomes of the Japanese NC.
These are discussed as follows:
(a) Exclusivity or insider-outsider (Uchi-Soto in Japanese) psychology by
which Japanese exclude anyone who is not an ethnic Japanese from
social discourse; (It is different from color or religious exclusivities. For
example, the Chinese or Koreans, who are living in Japan for centuries,
are excluded from the Japanese social circles.)
(b) Conformity or the doctrine of “nail that sticks up should be beaten
down”(Deru Kuiwa Utareru in Japanese) — deviations from the mainstream
norms are not tolerated;
(c) Seniority system (Senpai-Kohai in Japanese) by which every junior
must obey and show respects to the seniors;
(d) Collectivism in decision-making process (“Hou-Ren-Sou” system in
Japanese) and
(e) Continuous improvements (Keizen in Japanese), which is the fundamental
philosophy of the Japanese society.
These MEVs are exclusively Japanese, a reflection of the unique
Japanese culture (Basu, 1999; Nakane, 1970) and is fundamental to the
Japanese organizations.

144 Victoria Miroshnik
National culture construct along with the MEVs affect both the organizational
culture construct (OR), HRM system and leadership styles (LS)
constructs. Japanese OR construct is affected by the NC, MEVs, and the
HRM system. The similarities in OCs in different companies are due to
the similarities in NC and MEV; the differences are due mainly to the differences
in HRM. In Japan human resource practices vary from one company
to another and as a result, OCs and performances vary. In Toyota,
it is very consistent and strong culture with great emphasis on discipline,
Keizen, TQM and just in time (JIT) production-inventory system.
In many other companies in Japan, situations are not the same; as a result,
OC differs.
Organizational culture is affected by the NC, MEVs, and HRM. If the
company’s leader is also the founder, then only the leadership style (LS) can
affect the HRM and OC. Otherwise, when the leaders are professional managers
trained and grown up within the company (In Japan and in Japanese
companies abroad, it is out of practice to accept an outsider for the executive
positions. All executives enter the company after their graduation and
stay until they retire), appropriate LCs are developed by the OC and HRM.
Due to the collective decision-making process (Hou-Ren-Sou) leadership,
a MEV in the model, cannot affect an organizational culture or the
HRM system. It is very different from the Western (America, European,
or Australian) companies where the leaders are hired from outside and are
expected to be innovative regarding the OC and HRM system. This is quite
alien to the Japanese culture. Leadership style in Japan is an outcome, not
an independent variable as in the Western companies. Leadership style is
affected by the NC, MEVs, OC, and the HRM.
Organizational culture (OC) is affected by four factors, according to this
proposed model. These factors are: (a) stability; (b) flexibility; (c) internal
focus and (d) external focus (Cameron and Quinn, 1999). These factors are
universal, not restricted to the Japanese companies. However, how an OC
is being affected by NC, MEVs, and HRM would vary from country to
country.
Leadership style is a function of four factors. These factors are leader:
(a) as a facilitator; (b) as an innovator; (c) as a technical expert and (d) as
an effective competitor for rival firms (Cameron and Quinn, 1999). These
four characteristics of a leader are universal, but the emphasis varies from
country to country.
Finally, the corporate performance (CP) is affected by a number of
influencing factors: (a) customers’ satisfaction, (b) employees’ satisfaction

Toward a Theory of Japanese Organizational Culture 145
MAV
LC
CP
NC
OC
MEV
MIV
HRMPJ
Where “NC” is “National Culture”; “OC” is “Organizational Culture”; “LC” is “Leader
Culture”; “MAV” is “Macro-Values of Culture”; “MEV” is “Meso-Values of Culture”;
“MIV” is “Micro-Values of Culture”; “HRMPJ” is “Human Resources Management
Practices in Japan”, and “CP” is “Corporate Performance”.
Figure 2.
Value–culture–performance: a thematic presentation.
and commitments, and (c) the contribution of the organization to the society.
If we consider the contribution of the organization to society that is
already taken into account by the customers’ satisfaction and employees’
satisfaction, then CP has these two important contributory factors.
Theoretical relationship between the observed variables and the underlying
constructs are specified in an exploratory model, represented in Fig. 2.
In Fig. 3, a more elaborate model, including the unique HRM system of the
Japanese companies is described. Figure 3 represents a Linear Structural
Relations (LISREL) version (Joreskog and Sorbom, 1999) of the model,
which can be estimated using the methods of structural equation modeling
(Raykov and Marcoulides, 2000).
5. Discussion
The proposed theory describes the relationship between NC and CPs
through OC with the HRM system affecting the nature of the culture and
leadership. These inter-relationships are important aspects of the Japanese
corporate behaviors in a multinational setting and this proposed theory is
an attempt to understand the Japanese corporate culture.
Analysis of the Japanese culture and organizations by outsiders so far
suffers from a number of defects (Ikeda, 1987; Watanabe, 1998). They neither
try to understand the effects of the Japanese value system on their
organizations nor do they give any importance to the relationship between

146 Victoria Miroshnik
A1
A2
A3
D1
D2 D3 D4
B1
B2
B3
MAV
NC OC
LC CP
H1
B4
MEV
MIV
G1 G2 G3 FG
F6
H21
C1 C2 C3 C4 C5
HRMPJ
F1
F2
F3
F4
F5
E1
E24
Where “NC” is “National Culture”; “OC” is “Organizational Culture”; “LC” is “Leader Culture”;
“MAV” is “Macro-Values of Culture”; “MEV” is “Meso-Values of Culture”; “MIV” is
“Micro-Values of Culture”, and “CP” is “Corporate Performance”; A1 “Religious Values”, A2
“Moral Values” A3 “Habitual Values” are indicators for MAV variable; B1 “Power Distance”,
B2 “Individualism/Collectivism”, B3 “Masculinity/Femininity” are indicators for NC variable;
C1 “Uchi/Soto Value”, C2 “Deru Kuiwa Utareru Value”, C3 “Senpai/Kohai Value”, C4
“Hou-Ren-Sou Value”, C5 “Kaizen Value” are indicators for MEV variable; D1 “Stability”,
D2 “Flexibility”, D3 “External Focus”, D4 “Internal Focus are indicators for OC variable”;
E1 “On-Job-Training”; E2 “Emphasis on Personality of Recruits” are indicators for HRMPJ
variable; F1 “Sense of Belonging to a Group Value”, F2 “Respect and Recognition from Others
Value”, F3 “Sense of Life Accomplishment Value”, F4 “Self-respect Value”, F5 “Kangaekata
Value”, F6 “Ishiki Value” are indicators for MIV variable; G1 “Leader as Facilitator”, G2
“Leader as Innovator”, G3 “Leader as Technical Expert”, G4 “Leader as Competitor” are
indicators for LC variable; H1 “Customers Satisfaction”, H2 “Employees satisfaction and
Commitment” are indicators for CP variable.
Figure 3. Research model: Values-culture-performance (VCP): predicted paths
between variables and indicators.
performance and culture. So far, the success of the Japanese companies was
analyzed only in terms of their unique production and operations management
system. However, the inter-relationship between the production and
operations management system, which is a part of the OC, and the specific
HRM system it requires for its proper implementation, was not given
sufficient attention.
The typical example is the analysis of the failure of the implementations
of Japanese operations management system in Britain by Oliver and
Williamson (1992) or in China by Taylor (1999). They could not explain
the reason for the failure, as they have not analyzed the Japanese OC and
particularly the HRM system.

Toward a Theory of Japanese Organizational Culture 147
In a Japanese company, the LSs and the OC are designed by the HRM
system; these are not coming from outside. An effective corporate performance
is the result of these underlying determinants of OC and LSs. Thus,
in a Japanese organization, LS is rooted in the HRM system, which emerges
from the MEVs of the Japanese national culture.
Whether efficient CPs can be repeated in foreign locations depends on
the transmission mechanism of the Japanese OC, which in turn, depends on
the adaptations of the Japanese style HRM system. This can face obstacles
due to the different MEVs in a foreign society and as a result, OC in a
foreign location may be different from the OC of the company in Japan.
Adaptation of the operations management system alone will not create an
effective performance of a Japanese company in a foreign location. Creation
of an appropriate HRM system and appropriate OC are essential for an
effective performance.
6. Conclusion
A proposed theory of the relationship, among NC, OC, human resources
practices, and CPs for the Japanese multinational companies, is narrated.
Cultural differences are important and these factors affect every component
of the company behaviors and performances. The question was raised
regarding the factors, which are relatively more important than the others
and whether it will be possible to manipulate these factors in order to
increase the performances of the multinational companies. The proposed
theory may provide an answer to these issues.
References
Aoki, M (1990). Towards an economic model of the Japanese firm. Journal of Economic
Literature 28, 1–27.
Axel, M (1995). Culture-bound aspects of Japanese management. Management International
Review 35(2), 57–73.
Barlett, CA and H Yoshihara (1988). New challenges for Japanese multinationals: is organization
adaptation their Achilles Heel. Human Resources Management 27(1), 19–43.
Basu, S (1999). Corporate Purpose. New York: Garland Publishers.
Calori, R and P Sarnin (1991). Corporate culture and economic performance: a French study.
Organization Studies 12(1), 49–74.
Cameron, KS and R Quinn (1999). Diagnosing and Changing Organizational Culture:
Based on the Competing Values Framework. New York: Addison-Wesley.
Denison, DR and AK Mishra (1995). Toward a theory of organizational culture and effectiveness.
Organizational Science 6(2), March–April, 204–223.

148 Victoria Miroshnik
Fujino, T (1998). How Japanese companies have globalized. Management Japan 31(2),
1–28.
Hofstede, G (1980). Culture’s Consequences: International Differences in Work-related
Values. Beverly Hills, CA: Sage.
Hofstede, G (1985). The interaction between national and organisational value system.
Journal of Management Studies 22(3), 347–357.
Hofstede, G (1990). Measuring organizational cultures: a qualitative and quantitative study
across twenty cases. Administrative Science Quarterly 35, 286–316.
Hofstede, G (1993). Cultural constraints in management theories. Academy of Management
Executive 7(1), 81–94.
House, RJ et al. (1999). Cultural influences on leadership: Project GLOBE. In Advances in
Global Leadership, W Moblet, J Gessner and V Arnold (eds.), Vol. 1. Greenwick: CT,
JAI Press, 171–234.
Ikeda, K (1987). Nihon oyobi nihonjin ni tsuiteno imeji (Image of Japan and Japanese). In
Sekai wa Nihon wo Dou Miteiruka (How Does the World See Japan). A Tsujimura,
K Furuhata and H Akuto (eds.) Tokyo: Nihon Hyoronsa, pp. 12–31.
Imai, M (1986). Kaizen: The Key to Japan’s Competitive Success. New York, NY:
McGraw-Hill.
Joreskog, KG and D Sorbom (1999). LISREL 8.30: User’s Reference Guide. Chicago:
Scientific Software.
Kahle, LR, RJ Best and RJ Kennedy (1988). An alternative method for measuring valuebased
segmentation and advertisement positioning. Current Issues in Research in
Advertising 11, 139–155.
Kilman, R, MJ Saxton, and R Serpa (1985). Introduction: five key issues in understanding
and changing culture, In Gaining Control of the Organizational Culture, R Kilman,
M Gaxton and R Serpa (eds.), San Francisco: Jossey-Bass, pp. 1–16.
Kobayashi, N (1980). Nihon no Takokuseki Kigyo (Japanese multinational corporations).
Tokyo: Chuo Keizaisha.
Kotter, JP and JL Heskett (1992). Corporate Culture and Performance. NY: The Free Press.
Kujawa, D (1979). The labour relations of US multinationals abroad: comparative and
prospective views. Labour and Society, 4, 3–25.
Kumagai, F (1996). Nihon Teki Seisan Sisutemu in USA (Japanese Production System in
USA). Tokyo: JETRO.
Kumazawa, M and J Yamada (1989). Jobs and skills under the lifelong Nenko employment
practice. In The Transformation of Work. S Wood (ed.). London: Unwin Hyman, 56–79.
Marcoulides, GA and RH Heck (1993). Organization culture and performance: proposing
and testing a model. Organization Science 14(2), May, 209–225.
Morishima, M (1996). Renegotiating psychological controls, Japanese style. In Trends in
Organizational Behavior. CL Cooper (ed.), Vol. 3. NewYork: John Wiley & Sons Ltd.,
149–165.
Morita, A (1992). A moment for Japanese management. Japan-Echo 19(2), 1–12.
Miyajima, H (1996). The evolution and change of contingent governance structure in the
J-firm system: An approach to presidential turnover and firm performance. Working
Paper No. 9606. Institute for Research in Contemporary Political and EconomicAffairs.
Tokyo: Waseda University.
Nakane, G (1970). Japanese Society. Harmondsworth: Penguin.

Toward a Theory of Japanese Organizational Culture 149
Oliver, N and B Wilkinson (1992). The Japanization of British Industry. Cambridge,
Massachussets: Blackwell.
Ouchi, W (1981). Theory Z: How American Business can Meet the Japanese Challenge.
Reading, MA: Addison-Wesley.
Raykov, T and GA Marcoulides, (2000). A First Course in Structural Equation Modeling.
London: Lawrence Erlbaum.
Schein, EH (1997). Organizational Culture and Leadership. San-Francisco: Jossey-Bass
Publishers.
Shimada, H (1993). Japanese management of auto-production in the United States: An
overview of human technology in international labour organization. In Lean Production
and Beyond, Geneva: ILO, 23–47.
Taylor, B (1999). Patterns of control within Japanese manufacturing plants in China: doubts
about Japanization in Asia. Journal of Management Studies 36(6), 853–873.
Watanabe, S (1998). Manager-subordinate relationship in cross-cultural organizations: the
case of Japanese subsidiaries in the United States. International Journal of Japanese
Sociology 7, 23–43.

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Topic 3
Health Service Management Using
Goal Programming
Anna-Maria Mouza
Institute of Technology and Education, Greece
1. Introduction
Private production units usually operate on the basis of profit maximization.
However, to face competition from similar units and to be in line with some
major socio-economic factors, some decision makers are forced to relax this
basic objective. In order to present propositions for optimal management
decisions, one should combine the priorities of the decision maker with the
technical and socio-economic factors, which are involved in the operating
process in the best possible way. The production unit considered in this
paper is a relatively small (60 beds) private clinic in northern Greece, which
is similar to the orthopedic department of a hospital studied and described
elsewhere (Mouza, 1996).
However, in this particular case, there is no out-patient services. To
facilitate the presentation, I consider a five-year operational plan where
the personnel claims, the manpower working pattern, the various expenses,
together with the profit maximization target, and the expected number of
patients are described in detail. The necessary projections are based on
reliable techniques presented elsewhere (Mouza, 2002; 2006).
After setting the priorities of the various targets, I formulate a proper
“goal programming” problem using deviational variables (di
− and d
i + ) and
obtained the first-run solution. Then, I proceed to the goal attainment evaluation,
which dictated a re-adjustment of the priorities. The second-run
solution indicates that a slower acceleration of the profit maximization rate
is preferable, to avoid over-charging the patients, at the same time satisfying
most of the requirements for personnel management. Furthermore, if the
decision maker’s preference is relatively rigid, a lower rate of the increase
151

152 Anna-Maria Mouza
of salaries of the employees should be adopted. All computational results
are presented at the end of the relevant section.
2. The Details of the Private Clinic in Relation
to the Five-Year Plan
In Table 1, I present the composition of the personnel, and their salary
at the base year (t 0 ). Note that the 5-year planning horizon, refers to the
time-periods (years) t 1 , t 2 , t 3 , t 4 , and t 5 .
In columns 4 and 5 of Table 1, the total amount of the wages for all
employees of the same group, for the initial and final year is stated. Note
that the wages are an average of the salaries earned by each person in
the individual group. For each group, an average percent of annual salary
Table 1.
Personnel of the orthopedic clinic and their wages.
Groups
Position of the
group members
Members
at each
group
Annual salary at
year t 0 for all
group members
(in thousand )
Salary at final
year t 5 , for all
group members
(in thousand )
1 Orthopedic surgeons, 10 260 356.222
anaesthiologists and
microbiologists
2 Pharmacist 1 24.7 33.054
3 Operating-room nurses 3 54.6 68.04
4 Nurses plus laboratory 14 163.8 199.29
staff
5 Axial-tomography and 3 58.5 74.307
X-ray technicians
6 Clinic manager 1 27.3 36.190
7 Secretary and
3 32.76 39.476
administrative
service staff
8 Office clerks 4 41.6 49.647
9 Cooking and food 4 42.64 50.643
service staff
10 Other staff (guard,
bearers maintenance,
cleaning service etc.)
10 101.4 119.851

Health Service Management 153
increase, say R i , is considered. It should be noted that in some groups, this
rate is well above the rate of inflation growth, and the rate stated in the
collective wage and salary agreements for each employees group. These
rates of annual salary increase for all groups are presented in Table 3.
Denoting by A 0 (i) the annual salary of all members of group i at the base
year t 0 , and the final annual salary at year t 5 for all members of the same
group, denoted by A n (i), is computed from:
(
A n (i) = A 0 (i) 1 + R ) 5
i
. (1)
100
Thus for group 1, where R 1 = 6.5%, the final salary for all group members
will be:
A n (1) = 260(1 + 0.065) 5 = 356.222.
It should be noted, that these rates of salary increases have been formed
in accordance to the personnel claims. Other additional expenses for the
final year of of the planning period are presented in Table 2.
On the top of Table 2, the forecast regarding the expected number
of patients for the final year is stated. It should be pointed out that not
all patients necessarily need an axial-tomography and/or X-ray treatment.
That is why the average per patient cost stated in Table 2 seems to be
relatively low.
The interactive voice response (IVR) systems which are effectively used
in healthcare and hospitals are described by Mouza (2003). It should be
noted that replacement expenses together with expenses for obtaining new
devices, seems more reasonable to be equally distributed over the five years
of the planning period. Needless to say, that in case of replacements, the
estimated salvage on old equipment has to be subtracted from the relevant
cost. Thus, at the final year, only one fifth of such expenses is stated. For the
case under consideration, the replacement refers to the server of the local
area computer network (LAN), together with two stations. Their net cost
sum up to 2000, which has been equally spread over the five years of the
planning period.
From Table 1, I computed the average salary per employee at the final
year which, when multiplied by the group size gives the total salary for the
corresponding group, as it can be verified from Table 3.
It can be seen from Table 3, that X i (i = 1,...,10) denotes the size (i.e.,
the members) of group i and c i , the average salary of each group member.
Thus, the total salary of all the members of group 1, for instance, can also

154 Anna-Maria Mouza
Table 2.
final year.
Forecasted number of patients and various expenses for the
Patient expenses
Forecasted average
per patient, at the final
period t f ( )
Forecasted number of patients for the period (year) t 5 = 3625
Axial-tomography 9.1
X-ray 5.7
Medical supplies 59.4
Administrative and
32.1
miscellaneous
Other expected
Total ( ) Amount for the final year t 5
expenses
Installation of IVR
3000 600
system
Server and computers 2350 (salvage value: 350) 400
replacement
Personnel insurance
(19% of total
Endogenous (decision
variable X 39 )
salaries)
Laboratory expenses 60,000
Fixed expenses plus
180,000
depreciation
All other expenses 80,000
be computed from:
c 1 × X 1 = 35622.2 × 10 = 356222.
If I denote by X 10+i , the salary expenses of group i, then I may write
X 10+i = c i × X i (i = 1,...,10). (2)
so that the total salary expenses for the final year can be determined by
evaluating the summation:
20∑
i=11
X i . (3)

Health Service Management 155
Table 3.
Employees’salary at the initial and final year of the planning period.
Groups (i)
Number
of group
members
(X i )
Annual
salary at
year t 0 ,for
all the
members of
group i (in
thousand )
Annual
rate of
increase,
R i (in %)
R i
Salary at
final year t f ,
for all the
members of
group i
(in )
Average
per person
at each
group (c c i )
1 10 260 6.5 356,222 35,622.2
2 1 24.7 6 33,054 33,054
3 3 54.6 4.5 68,040 22,680
4 14 163.8 4 199,290 14,235
5 3 58.5 4.9 74,307 24,769
6 1 27.3 5.8 36,190 36,190
7 3 32.76 3.8 39,476 13,158.666
8 4 41.6 3.6 49,647 12,411.75
9 4 42.64 3.5 50,643 12,660.75
10 10 101.4 3.4 119,851 11,985.10
Another point of interest refers to the average working hours of the
members of each group. The relative figures are analytically presented in
Table 4.
It can be easily verified that in Table 4, column 5 is obtained by multiplying
the elements of column 4 by 52.
Denoting by X 22+i (i = 1,...,10) the total average working hours per
year for all the group members, then I may write
X 22+i = w i × X i (i = 1,...,10). (4)
3. The Nature of the Problem
Given all the information presented in Tables 1–4, the resultant problem
is, how to formulate a feasible operating plan, which should combine
the desired salary increases and the full utilization of working hours,
the expenses incurred, together with the desired gross profit at the final
year set by the decision maker, in the best possible way with the minimum
sacrifice. This problem can be answered by the goal programming
method, originally developed by Charnes and Cooper (1961). It should

156 Anna-Maria Mouza
Table 4.
Working hours of each group personnel.
Groups (i)
Number
of group
members
Hours per
week
(average),
for each
member of
group i (in
thousand )
Total hours
per week
for all the
members of
group i
Total
hours per
year, for
all the
members
of each
group
Average
per person
at each
group (w i )
1 10 65 650 33,800 3380
2 1 45 45 2340 2340
3 3 65 195 10,140 3380
4 14 40 560 29,120 2080
5 3 40 120 6240 2080
6 1 45 45 2340 2340
7 3 40 120 6240 2080
8 4 40 160 8320 2080
9 4 30 120 6240 1560
10 10 30 300 15,600 1560
be recalled that goal programming is a mathematical programming technique
with the capability of handling multiple goals given certain priority
structure. Furthermore, a goal programming model may be composed of
non-homogeneous units of measure, which is the case under consideration.
In brief, the main task here refers to the compensation of total expenses
with the decision maker’s requirement regarding gross profits, without any
change in the operating pattern of the clinic, as far as the manpower level is
concerned.
3.1. Specification of the Problem Decision Variables
• The first 10 decision or choice variables X i (i = 1,...,10) are
already defined in Table 3 and refer to the number of personnel in
group i.
— Variables X 11 ...X 20 , stand for the salary cost of each group.
— Variable X 21 denotes total salary cost at the final year.
— Variables X 22 ...X 31 refer to the total working hours, observed in
the 5th column of Table 4.

Health Service Management 157
• Variables X 32 ...X 35 refer to the average cost per patient, as it is stated
in the first four rows of Table 2.
— Variable X 36 denotes total per patient expenses.
— Variables X 37 and X 38 refer to the equipment purchase and
replacement.
• Variable X 39 stands for the personnel insurance expenses.
— Variable X 40 refers to the depreciation, laboratory, fixed and other
expenses.
• Variable X 41 is used to sum up all the above expenses (i.e., X 37 + X 38 +
X 39 + X 40 )
• X 42 , which also is a definition variable, is used to denote total operating
cost for the final year t f (i.e., t 5 ) of the planning period.
• Finally, variable X 43 denotes the average charge per patient, so that the
desired gross profit would not be less than 750,000.
3.2. Formulation of the Constraints (Goals)
To facilitate the presentation, I classified the goals into the following seven
categories.
3.2.1. Personnel Employed
The operation pattern of the clinic, regarding the personnel employed is
presented in Table 1. Given that, the decision maker does not want to alter
this pattern, I must first introduce the following 10 constraints (goals)
X i + d − i
− d + i
= b i (i = 1,...,10) (5)
where b 1 = 10, b 2 = 1, b 3 = 3, b 4 = 14, b 5 = 3, b 6 = 1, b 7 = 3, b 8 = 4,
b 9 = 4 and b 10 = 10, are the desired targets, regarding the members of
each group as shown in Tables 1, 3 and 4.
It is useful to recall that di − and d
i + denote the so-called deviational
variables from the goals, which are complementary to each other, so that
di − × d
i + = 0. If the ith goal is not completely achieved, then the observed
slack will be expressed by di − , which represents the negative deviation from
the goal. On the other hand, if the ith goal is over achieved, then d
i
+ will
take a non-zero value. Finally, if this particular goal is exactly achieved,
then both di − and d
i + will be zero.

158 Anna-Maria Mouza
3.2.2. Personnel Claims for Salary Increase
According to Eq. (2), I have to introduce the following 10 constraints in
order to define the total salary expenses for each group.
X 10+i − c i X i + d10+i − − d+ 10+i
= 0, (i = 1,...,10). (6)
It is recalled that coefficients c i are presented in Table 3. An additional
variable X 21 is introduced to sum up salary expenses for all personnel at
the final year. The computation of this total is based on Eq. (3).
X 21 −
20∑
i=11
X i + d21 − − d+ 21
= 0. (7)
3.2.3. Complete Utilization of Personnel Capacity in Terms
of Working Hours
The forecasted number of patients for the final year is not exceeding the
clinic capabilities, regarding the existing infrastructure. Furthermore, the
decision maker does not want to alter the existing operation pattern, since
he considers that the present personnel manpower potential will be adequate
to provide satisfactory service to the number of patients forecasted,
provided that the under utilization of the regular working hours will be
avoided. Hence, I introduced the following constraints in accordance to
Eq. (4), which on the other hand may be regarded as a measure to provide
job security to all personnel by avoiding underutilization of their regular
working hours as shown in Table 4.
X 21+i − w i X i + d21+i − − d+ 21+i
= 0, (i = 1,...,10). (8)
Note, the co-efficients w i , are also presented in Table 4.
3.2.4. Patient expenses
The axial-tomography expenses per patient can be expressed as:
X 32 + d32 − − d+ 32 = 9.1.
X-ray expenses per patient:
X 33 + d33 − − d+ 33 = 5.7.
Medical expenses per patient:
X 34 + d34 − − d+ 34 = 59.4.
(9a)
(9b)
(9c)

Administrative and miscellaneous expenses per patient:
Health Service Management 159
X 35 + d − 35 − d+ 35 = 32.1.
Variable X 36 depicts total per patient expenses at the final year.
X 36 − (X 32 + X 33 + X 34 + X 35 ) + d − 36 − d+ 36 = 0.
(9d)
(9e)
3.2.5. Other Expected Expenses
Installation of the IVR system.
Computers and server replacement.
X 37 + d − 37 − d+ 37 = 600.
X 38 + d − 38 − d+ 38 = 400.
(10a)
(10b)
The insurance funds.
From Table 2, we see that the average expenses for personnel insurance
amounts to 19% of the total employees’ salary. This is represented by the
following constraint, taking into account the variable X 21 .
X 39 − 0.19X 21 + d − 39 − d+ 39 = 0
Depreciation, laboratory, fixed and other expenses
X 40 + d40 − − d+ 40
= (60,000 + 180,000 + 80,000). (10d)
To sum all other expenses, I introduce the following relation.
X 41 − (X 37 + X 38 + X 39 + X 40 ) + d − 41 − d+ 41 = 0.
(10c)
(10e)
3.2.6. Total Expenses
It is already mentioned that I introduce the variable X 43 in order to sum up
total expenses, in the following way.
X 42 − (X 21 + 3625X 36 + X 41 ) + d42 − − d+ 42
= 0. (11)
3.2.7. Total Gross Profit
The gross profit achievement as set by the decision maker, may be introduced
in the following way.
3625X 43 − X 42 + d43 − − d+ 43
= 750,000 (12)

160 Anna-Maria Mouza
where X 43 , as it was mentioned earlier, represents the adequate charge per
patient, in order to satisfy Eq. (12). It is recalled that the coefficient 3625,
which appears in Eq. (11) too, is the stated forecast, regarding the expected
number of patients for the final year t f .
With the above formulation, we see that the number of constraints is
equal to the number of choice variables (43).
3.3. Priority of the goals — The objective function
It is obvious that the decision maker, apart from determining the goals of
the five-year plan, also has to specify the priorities (Gass, 1986), denoted by
P i , in order to accomplish the optimum allocation of resources for achieving
these goals in the best possible manner. One further point, that has to
be considered in the formulation of the model, is the possibility of weighing
the deviational variables at the same priority level (Gass, 1987). The
list of decision maker’s goals is presented below in descending order of
importance.
1. To retain the present operating pattern of the clinic.
This implies that no alterations are desired regarding the number and
composition of the existing personnel (P 1 ). Different weights have been
assigned to the various personnel groups.
2. To achieve the desired level of gross profits. Also, to provide reserves for
the personnel insurance, to cover all expenses for equipment replacements
and installation of a new IVR system (P 2 ).
3. To avoid underutilization of the personnel regular working hours, providing
at the same time job security to all employees (P 3 ).
4. To provide the funds necessary to cover all patient’s expenses (P 4 ).
5. To provide adequate funds for covering laboratory and fixed expenses,
depreciation etc. (P 5 ).
6. To provide the wage increase, claimed by the personnel at the various
groups (P 6 ).
In this case, weights are used to discriminate the salary increase of
each group. Heavier weights have been assigned to groups with lower
salaries.
According to the above ranking of the goals priority and taking into
account the relations for the corresponding totals, the following objective

Health Service Management 161
function is formulated.
min z = (10P 1 d − 1 + 9P 1d − 2 + 8P 1d − 3 + 7P 1d − 4 + 6P 1d − 5 + 5P 1d − 6
+ 4P 1 d − 7 + 3P 1d − 8 + 2P 1d − 9 + P 1d − 10 ) + (P 2d − 37 + P 2d − 38
+ P 2 d − 39 + 3P 2d − 42 + P 2d − 43 ) + P 3
31∑
i=22
di − ∑36
+ P 4
i=32
+ (P 5 d − 40 + P 5d − 41 ) + (P 6d − 21 + 2P 6d − 11 + 2P 6d − 12 + 3P 6d − 13
+ 4P 6 d − 14 + 5P 6d − 15 + 6P 6d − 16 + 7P 6d − 17 + 8P 6d − 18
+ 9P 6 d19 − + 10P 6d20 − ). (13)
d − i
4. Initial Results
With this specification of the goal programming model, I obtain the results
as given on the left side of Table 5 (solution I). It is easily verified that all
goals are achieved. Hence, this pattern dictated by the optimal solution is
readily applicable. It should be pointed out that according to this solution,
an average rate of total salary increase of about 4.9% is realized, whereas
the mean salary per worker increases from 15,232.1 to 19,372.1. In fact, this
average rate r (i.e., 4.9) has been computed from Eq. (1) in the following
way, using natural logs.
ln(x)
5
= ln(1 + r), where x = 1,026,720
807,300
and r = (y − 1) × 100, where y = e Z and Z = ln(x)
5
However, the charge per patient (∼740 ) is considered being higher,
when compared to the average of the local market, affecting thus the
competition level of the clinic.
5. Imposition of a New Constraint
Given the social character of health service, which has to be combined with
the fact that the unit under consideration must be competitive, it is necessary
to impose the following constraint.
X 43 + d44 − − d+ 44
= 700. (14)

162 Anna-Maria Mouza
Thus, the total number of constrains has become 44. It should be noted
that minimizing d
44 + in the objective function, an upper limit of 700 is
set to the average charge per patient. Hence, I added in the objective as in
Eq. (13) the following term
2P 2 d
44
+
which implies that the restriction regarding the maximum average charge
per patient has been considered as a second priority goal, properly weighed.
5.1. Second-Run Results
With the new constraint, the solution obtained is presented on the right
side of Table 5 (solution II). I observe that constraint Eq. (14) is binding,
and in order to achieve the level of gross profit set by the decision
maker, the solution dictates that the total salary expenses must be reduced
by 118,180.125, which is the value of the deviational variable d21 − , shown
in Eq. (7). Evaluating the results of the second run, one may argue as to
Table 5.
Solution I (left) and solution II (right).
No. Variable name Value No. Variable name Value
The simplex solution (Number of patients = 3625)
87 ×1 10.000 89 ×1 10.000
88 ×2 1.000 90 ×2 1.000
89 ×3 3.000 91 ×3 3.000
90 ×4 14.000 92 ×4 14.000
91 ×5 3.000 93 ×5 3.000
92 ×6 1.000 94 ×6 1.000
93 ×7 3.000 95 ×7 3.000
94 ×8 4.000 96 ×8 4.000
95 ×9 4.000 97 ×9 4.000
96 ×10 10.000 98 ×10 10.000
97 ×11 356,222.000 99 ×11 356,222.000
98 ×12 33,054.000 100 ×12 33,054.000
99 ×13 68,040.000 101 ×13 68,040.000
100 ×14 199,290.000 102 ×14 199,290.000
101 ×15 74,307.000 103 ×15 74,307.000
102 ×16 36,190.000 104 ×16 36,190.000
(Continued )

Table 5. (Continued )
Health Service Management 163
No. Variable name Value No. Variable name Value
The simplex solution (Number of patients = 3625)
103 ×17 39,476.000 105 ×17 39,476.000
104 ×18 49,647.000 106 ×18 49,647.000
105 ×19 50,643.000 107 ×19 50,643.000
106 ×20 119,851.000 108 ×20 119,851.000
107 ×21 1,026,720.000 21 d − 21
118,180.125
108 ×22 33,300.000 110 ×22 33,800.000
109 ×23 2340.000 111 ×23 2340.000
110 ×24 10,140.000 112 ×24 10,140.000
111 ×25 29,120.000 113 ×25 29,120.000
112 ×26 6240.000 114 ×26 6240.000
113 ×27 2340.000 115 ×27 2340.000
114 ×28 6240.000 116 ×28 6240.000
115 ×29 8320.000 117 ×29 8320.000
116 ×30 6240.000 118 ×30 6240.000
117 ×31 15,600.000 119 ×31 15,600.000
118 ×32 9.100 120 ×32 9.100
119 ×33 5.700 121 ×33 5.700
120 ×34 59.400 122 ×34 59.400
121 ×35 32.100 123 ×35 32.100
122 ×36 106.300 124 ×36 106.300
123 ×37 600.000 125 ×37 600.000
124 ×38 400.000 126 ×38 400.000
125 ×39 195,076.797 127 ×39 172,622.578
126 ×40 320,000.000 128 ×40 320,000.000
127 ×41 516,076.812 129 ×41 493,622.562
128 ×42 1,928,134.375 130 ×42 1,787,500.000
129 ×43 738.796 131 ×43 700.000
109 ×21 908,539.875
whether this is an optimal solution, from the socio-economic point of view,
since any reduction has to directly affect the employees salary solely. On
the other hand, the decision maker is not willing to entirely undertake this
reduction (118,180.125), decreasing gross profits by almost 16%. With all
these in mind, I present the following proposition, which may be considered
of particular importance.

164 Anna-Maria Mouza
6. Some Alternatives
After proper negotiations, the decision maker and the employees have to
agree on the proportion, say a (where 0

Table 7.
Salary at the initial and final years together with the annual rates of increase.
Groups (i)
Salary at the
period t 0 ( )
Initially
claimed
salary for the
final year ( )
Amount of
reduction
Salary to be
realized at the
final year ( )
Actual annual
rate of salary
increase (%)
New
coefficients c i
c i
1 260,000 356,222 37,090.172 319,131.81 4.1836 31,913.181
2 24,700 33,054 2859.187 30,194.81 4.0991 30,194.81
3 54,600 68,040 2942.746 65,097.25 3.5795 21,699.083
4 163,800 199,290 6384.697 192,905.3 3.3252 13,778.95
5 58,500 74,307 4082.711 70,224.29 3.7209 23,408.096
6 27,300 36,190 2689.870 33,500.13 4.1782 33,500.13
7 32,760 39,476 961.173 38,514.83 3.2897 12,838.278
8 41,600 49,647 858.898 48,788.10 3.2391 12,197.025
9 42,640 50,643 567.861 50,075.14 3.2669 12,518.785
10 101,400 119,851 652.748 119,198.25 3.2872 11,919.825
Health Service Management 165

166 Anna-Maria Mouza
increase for each group, the number of employees per group together with
the ranking scores, I computed the index presented in the 4th column of
Table 6. Multiplying the elements of this column by 59,090.0625, we get
the entries of the 5th column.
From the last column of Table 6, I computed the end period salary
of each group and the corresponding annual rate of increase, which are
presented in Table 7.
From Table 7, we can see that the requirement for the annual rate of
salary increase at each group to exceed 3.1%, is fully satisfied. In an opposite
situation however, one has to reduce the value of “a” by, say, 0.05 and
to repeat all calculations. It should be also noted that with the allocation
proposed so far, total initial salary, spending will increase by an annual
rate of 3.69% (from 807,300 to 967,629.9) and the annual wage per capita
will increase by 19.86% (from 15,232.1 to 18,257.2). It is clear that all
employees will be better off with smaller value of a. The composite index
and all other entries of Tables 6 and 7 can be computed with the following
code segment written in Visual Fortran.
MODULE data_and_params
! Goups=number of groups ! Planning_hor=Planning horizon (years)
! R = Initial rate of salary increase at each group (vector)
! Members = Number of employees at each group (vector)
! Salary_in = Initial employees salary at each group (vector)
! Salary_f = Final claimed salary for each group (vector)
! Deficit = The value of deviational variable
! a = Value of coefficient a (0

Health Service Management 167
WRITE(out,*)’ Composite index and the final rate of salary increase’
WRITE(out,’(/)’)
Deficit=Total_Deficit*a ; sortR=R ; Salary=Salary_f/members
! Perform ranking operation
CALL SORTQQ(LOC(sortR),groups,SRT$REAL4)
DO i=1,groups
s=R(i)
DO j=1,groups
IF(sortR(j) == s) scores(i)= j
ENDDO ; ENDDO
! Compute composite index
Rsmall=R/100. ; Y=Rsmall*Salary ; s=SUM(Y)
Employees=SUM(Members)
rate=(y*100)/s/100. ; X=rate*deficit/Employees
s=SUM(X)
rate=(x*100.)/s/100. ; s=SUM(X) ; X=rate*Members
s=SUM(X)
Rate=(X*100.)/s/100. ; s=SUM(Rate) ; X=rate*scores
s=SUM(X)
rate=(X*100)/s/100. ; s=SUM(rate) ; X=Deficit*rate
! Compute revised annual rates of salary increase
Y=Salary_f-X
Logvector=(LOG(Y/Salary_in))/ planning_hor
newrate=(EXP(logvector) -1.)*100.
WRITE(out,*) ’ Index Reduction Final Salary New rate’
DO i=1,groups
WRITE(out,’(1X,F9.6,2X,F10.3,4X,F10.2,6X,F6.4)’) Rate(i)&
&, X(i), Y(i), newrate(i)
ENDDO
END
7. Final Results
In the last column of Table 7, the revised coefficients c i are stated. These
new coefficients are to be considered in Eq. (2), and in the corresponding
restrictions seeing in Eq. (6) for the final run. Also, the objective in Eq. (13)
has been slightly reformed as follows:
min z = (10P 1 d1 − + 9P 1d2 − + 8P 1d3 − + 7P 1d4 − + 6P 1d − 5 + 5P 1d6
−
+ 4P 1 d − 7 + 3P 1d − 8 + 2P 1d − 9 + P 1d − 10 ) + (P 2d − 37 + P 2d − 38
+ P 2 d − 39 + 3P 2d − 42 + 2P 2d + 44 ) + P 3
31∑
i=22
di − ∑36
+ P 4
+ (P 5 d − 40 + P 5d − 41 ) + (P 6d − 21 + 2P 6d − 11 + 2P 6d − 12
i=32
+ 3P 6 d − 13 + 4P 6d − 14 + 5P 6d − 15 + 6P 6d − 16 + 7P 6d − 17 + 8P 6d − 18
+ 9P 6 d − 19 + 10P 6d − 20 ) + P 7d − 43 .
d − i

168 Anna-Maria Mouza
The solution obtained with the re-stated restrictions satisfies all requirements.
Now, total expenses sum up to 1,857,817.125. It has to be underlined,
however, that since the value of the deviational variable d43 − is
70,317.2, it is implied that total gross profits undergo a reduction of about
9.38% (from 750,000 to 679,682.8), which is a bit higher when compared
to the corresponding percentage (∼6%) of total salary reduction. Nevertheless,
the results provide a sound basis to achieve an optimal solution, in the
sense that it is acceptable by all people involved without any violations of
the existing rules.
8. Conclusions
Many clinics like the one presented here benefit the patients, the health
service in a convenient way, and help attain consistency and continuity
of treatment. These achievements are heavily dependent on a successful
budget planning. The characteristics of a model of this type for a clinic
are based upon many factors, such as the type of the clinic, the location,
the size, the medical specialty, etc. Hence, it is difficult to design a general
model that can be applied to all types of clinics. However, once a budget
planning model has been developed, it can be easily modified at a later
stage to fit many other types of clinics. With this in mind, I consider in this
paper an orthopedic clinic and implemented a model designed for a fiveyear
planning period, using the goal programming approach of aggregate
budget planning for this particular health care unit. To start with, the goals
and the relevant priorities are set in advance, to formulate the corresponding
goal programming model. The solution obtained is operational in the sense
that, through the analysis of resource requirements, the acceptable charge
per patient, the desired level of gross profits, the claimed rate of salary
increases by the employees, and the trade-offs among the set of goals are
achieved with a minimum sacrifice. The model shows that this sacrifice is
negotiable between different sides, so that the business manager can finally
establish an aggregative budget planning with the best perspectives, since
the realization of a fair wage policy can be obtained through using the
composite index, introduced in this paper.
References
Charnes, A and W Cooper (1961). Management Models and Industrial Applications of
Linear Programming (Vols. 1 and 2). New York: Wiley.
Everett, JE (2002). A decision support simulation model for the management of an elective
surgery waiting system. Health Care Management Science 5, 89–95.

Health Service Management 169
Flessa, S (2000). Where efficiency saves lives: a linear programme for the optimal allocation
of health care resources in developing countries. Health Care Management Science 3,
249–267.
Gass, SI (1986). A process for determining priorities and weights for large scale linear goal
programming. Journal of Operational Research Society 37, 779–785.
Gass, SI (1987). The setting of weights in linear goal programming. Computers and Operations
Research 14, 227–229.
Mouza and Anna-Maria (1996). An economic approach of the Greek health sector, based
on domestic data. Modeling the hospital operation process. Ph.D. Theses, Greece:
Aristotle University of Thessaloniki.
Mouza and Anna-Maria (2002). Estimation of the total number of hospital admissions and
bed requirements for 2011: the case for Greece. Health Service Management Research
15, 186–192.
Mouza and Anna-Maria (2003). IVR and administrative operations in healthcare and hospitals.
Journal of Healthcare Information Management 17(1), 68–71.
Mouza and Anna-Maria (2006). A note regarding the projections of some major health
indicators. Quality Management in Health Care 15(3), 184–199.
Ogulata, SN and R Erol (2003). A hierarchical multiple criteria mathematical programming
approach for scheduling surgery operations in large hospitals. Journal of Medical
Systems 27(3), 259–270.

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Chapter 5
Modeling National Economies

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Topic 1
Inflation Control in Central and Eastern
European Countries
Fabrizio Iacone and Renzo Orsi
University of Bologna, Italy
1. Introduction
The recent accession to the European Union (EU) of 10 new members
officially opened the agenda of their participation in the European Monetary
Union (EMU) too.
Although, the accession of the new European partners to the euro-area
is formally analyzed, keeping the Maastricht criteria as the main reference,
these do not necessarily reflect the effective integration and convergence of
the economies. With this respect, we think it is important to study if and how
the Eurosystem can successfully control inflation after the extension of the
EMU: we then investigated the monetary policy transmission mechanism in
the Central and Eastern European Countries (CEECs) to see how compatible
it is with one of the current members of euro-area.
Knowledge of the mechanism of transmission of monetary policy is
also necessary to the CEECs to choose the monetary strategy for the period
preceding the accession to the euro-area. The discussion is open, both in
the literature and among monetary institutions, on whether a direct inflation
targeting or some kind of exchange rate commitment should be preferred:
by comparing the mechanism of transmission of policy impulses in different
regimes, we can see if a certain strategy made inflation control easier or
more difficult, and assess its cost by looking at the impact on the economic
activity.
We focused on Poland, Czech Republic, and Slovenia because they
are very different for the initial conditions from which they started the
transition to functioning market economies and later the integration in the
EU, for the relative size and the degree of openness to the international
trade, for the policies implemented in due course and even for their historical
173

174 Fabrizio Iacone and Renzo Orsi
developments: we think that because of these differences they are, together,
representative of the whole group of CEECs. For the euro-area, we took
Germany as the reference country.
2. Inflation Control over 1989–2004
2.1. Transition, Integration, and Accession
Although Poland, Czech Republic, and Slovenia shared the goals of implementing
a functioning market economy and of acceding to the EU, the
policies they implemented to reach them were rather different.
The first reason for the difference is in the productive structure at the
beginning of the transition. Yugoslavia established a quasi-market system
well before 1989, with quite independent firms and relatively hard budget
constraints; production was much more centralized and budget constraints
much softer in Poland and Czech Republic, and, to make things tougher for
these two countries, they also had to suffer the break-up of the council for
mutual economic assistance (CMEA), in which they were well integrated
(Czech Republic also had to endure the additional trade disruption, caused
by the separation from Slovakia). Poland and Czech Republic represent
an average position with respect to the general condition of the productive
structure of the CEECs at the beginning of the transition. Local differences
remain: for example, Hungary implemented some timid reforms before
1989, while the three Baltic countries experienced a much bigger shock,
because the disintegration of the Soviet Union resulted in the loss of their
largest trade partner. The stronger centralization, the softer budget constraint,
and the higher disruption caused by the break. up of the CMEA,
and of Czechoslovakia could have coeteris paribus caused a more turbulent
and longer transition for Poland and Czech Republic, but in reality Slovenia
had to face the major shock due to the collapse of Yugoslavia and of the
subsequent wars, which deprived the country of its biggest market and had
other adverse effects including the loss of revenues and hard currency due
to the fall of tourism.
A more precise ranking emerges when the size and the openness to
international trade is considered, with Poland being the largest country and
Slovenia the smallest one. As far as the monetary policies implemented for
inflation stabilization, all the CEECs except Slovenia, began their transition
with a strong commitment to a fixed exchange rate. The initial price
liberalization, in fact, left the system without a nominal anchor, and, also

Inflation Control in Central and Eastern European Countries 175
because of a natural price rigidity with respect to negative corrections, the
re-alignment of relative prices took the form of a sudden increase and a steep
inflation followed: by opening to the international trade (and by introducing
the proper legislation, in order to force the local producers to face a harder
budget constraint), the countries in transition had a chance to import a price
structure similar to the one of their commercial partners. In fact, being the
exchange rate fixed, the domestic producers could not raise their prices too
much without losing competitiveness with respect to the foreign ones.
Slovenia followed a different approach to disinflation, targeting the
growth of a relatively narrow monetary aggregate (M1); according to Capriolo
and Lavrac (2003), anyway the key characteristic of the period was the
continuous intervention on the foreign exchange market in order to prevent
an excessive real rate appreciation (contrary to the strategy of the Bundesbank
and of the Eurosystem, the control of M1 was also enforced with nonmarket
instruments and procedures). Since mainstream optimal currency
area literature prescribes a greater incentive to adopt a stable exchange rate
to the countries more open to the international trade, the fact that the outcome
is actually reversed means that price stabilization rather than trade
was the priority in the exchange rate commitment served in Poland and in
Czechoslovakia.
Fixing the exchange rate may have contributed to price stabilization,
and inflation actually dropped very quickly, but there are certain differences
remained with respect to the EU, leading to a strong real exchange rate
appreciation. This may have been partially due to the Balassa-Samuelson
effect: assuming that the marginal productivity and the wage in the sector
of internationally traded goods, is set on the foreign market and that the
same wage is transferred to the production of the non-traded goods, then
the productivity gap between the two sectors is compensated by a price
increase in the less productive domestic sector. This yields a progressive
appreciation of the real exchange rate and higher domestic inflation.
The faster growth of productivity, determined by the transfer of
technology from the international trade partners and the more efficient allocation
of the resources within the economies, compensated part of the pressure
on the domestic producers, but the fixed exchange rate arrangements
were not sustainable for a long time: Poland switched to a regime of preannounced
crawling peg as early as 1991, later coupling it with an oscillation
band which was gradually widened until it was finally abandoned in 2000;
Czech Republic resorted to a free float without explicit commitment as
early as 1997 under the pressure of a speculative attack, its currency having
progressively over-evaluated in real terms over time. Both the countries

176 Fabrizio Iacone and Renzo Orsi
replaced the monetary anchor by introducing a direct inflation target (Czech
Republic starting in 1998, Poland in 1999). The progressive weakening of
the exchange rate commitment took place in Hungary and Slovakia too, but
in these last two countries, the switch of targets was not complete: Hungary
retained a fixed exchange rate commitment, albeit with a very wide band,
while Slovakia did not implement an explicit inflation targeting because of
the high role that administrated prices still had in the consumer prices. Anyway
this is not an unanimous attitude: the three Baltic States kept a fixed
exchange rate with an extremely tight band, apparently trying to exploit the
credibility acquired with it during the first phase of the transition, and Estonia
even withstood a moderate speculative attack rather than devaluating.
Once again, Slovenia went in the opposite direction: according to Capriolo
and Lavraac, a more aggressive exchange rate strategy has been pursued
since 2001, with an active, albeit informal, crawling peg.
2.2. Exchange Rate and Direct Inflation Targeting
The fixed exchange rate played a key role in the stabilization phase; nowadays,
it is still the reference of monetary policy in the Baltic States, and it is
also present in Hungary. Since, the exchange rate commitment is also part of
the Maastricht criteria, where two years of participation to the exchange rate
mechanism (ERM) 2 is required, the decision of Poland, Czech Republic,
and Slovakia, to completely abandon it may indeed seem to be a paradox.
Surely, a small country cannot ignore the effect of the exchange rate
fluctuations on the stability of financial institutions and the economy as
a whole, but a commitment to a fixed parity is a much stronger policy.
Whether, macroeconomic stability and inflation control are helped or
hindered by this depends on the credibility of the commitment itself.
There can be little doubt that an exchange rate commitment is a risky
policy: the integration of the financial markets allows the mobilization of
large amounts of funds, and no central bank can muster enough foreign
exchange reserves to resist a sustained attack, nor indeed may desire to do
it, because the mere defence of the currency could require a substantial rise
in the domestic interest rates, for which the economy may be even more
detrimental than the devaluation that it was trying to prevent. Against an
exchange rate commitment, stands the evidence of speculative attacks in
the past: consider, for example, the break up of the ERM 1, when even
the French currency suffered some pressure, although the fiscal, financial,
and macroeconomic situation of the country was not worse than it was
in Germany. The same lesson can indeed be derived by looking at the

Inflation Control in Central and Eastern European Countries 177
Hungarian experience: when the two objectives were in conflict, as in June
2003, one had to be abandoned, and a devaluation took place.
Since the accession to the EU also required the complete adoption of
the acquis communautaire, thereby including the elimination of capital
controls, the apparent paradox of several CEECs switching to a free float
and inflation targeting, for the period preceding the adoption of the euro,
is then a strategy that may protect their currencies from unrealistic parities
and speculative attacks.
On the other hand, a direct inflation targeting can only be successful if
the monetary authority has earned itself a solid reputation, and this primarily
requires the independence from any political interference. Since the CEECs
only acquired a formal central bank independence in the last few years, as a
part of the process of adoption of the acquis communautaire, their credibility
may still be weak. Central bank independence is even more a concern,
when the definition is extended beyond the mere legal requirement: in most
of the cases for example, the credibility was seriously weakened because
the fiscal authority had the opportunity to partially finance its expenditures
through the central bank; political pressures, as experienced in the Czech
Republic and in Poland, may undermine the credibility of the central bank
even when they are resisted, because they may erode the consensus in
the country. Several indices of central bank independence, were proposed
in the literature: according to Maliszewski (2000), and to the extensive
survey in Dvorsky (2000), the CEECs were lagging behind with respect
to their Western counterparts, Poland and the Czech Republic faring better
than Slovenia. Indeed, it is exactly because the credibility of the monetary
authorities is lower in the CEECs that Amato and Gerlach (2002) proposed
to supplement the inflation targeting with a mild monetary commitment,
this would increase the information in the market.
It is then important to ascertain if the exchange rate commitment is a
risk worth taking, not only for the countries on the way to EMU that are still
more than two years away from the formal discussion of their convergence
according to the Maastricht criteria, but also for other emerging economies
in the world.
2.3. A Summary of the Results of Previous Analyses
Several empirical analyses on inflation control in CEECs appeared in the
recent years. Iacone and Orsi (2004) surveyed many applied works: these
varied for the country that was analyzed, for the period considered and for
the methodology adopted, making comparison rather difficult.

178 Fabrizio Iacone and Renzo Orsi
Interpretation of the results was often dubious because either the variables
of interest were replaced by first or second differences, or the intermediate
steps linking the monetary instrument to the target were omitted,
thus obscuring any potential evidence about the channel through which
inflation may be controlled. Reliability was also hampered by the fact that
in many cases no stability analysis was provided, despite the potentially
disruptive effects of the transition on the estimates, nor any attempt was
made to model the slow formation of a market economy despite this being
the main feature of the period.
It seems nevertheless fair to conclude that the exchange rate is very
important for the stabilization of inflation, an appreciation of the real
exchange rate reducing the growth rate of prices. The empirical evidence
supporting the existence of a standard interest rate channel was much more
controversial, the results depending largely on the econometric approach
and model adopted by the researcher and on the sampling period considered.
2.4. A Structural Model for Monetary Policy
It is possible that the weak support provided by these analyses is at least
partially due to the methodology adopted: VAR models have the advantage
of requiring a minimal structural specification, but, in return, they need
the estimation of many parameters. Considering the short length of the
sampling size and the potential extreme instability of the parameters due to
the transition, large standard errors and non-significant estimates seem to
be unavoidable consequences.
A structural model can provide a more parsimonious approach: we
followed Rude-bush and Svensson (1999) and considered the model
⎧
⎨ π t = α 0 + α π1 π t−1 + α π2 π t−2 + α π3 π t−3
+ α π4 π t−4 + α y y t−1 + ε π,t PC
⎩
y t = β 0 + β y y t−1 − β
AD
where y t is a measure of the economic activity, π t is the annualized inflation
within the quarter, it is a short-term interest rate, ¯π =
4 1 ∑ 3j=0
π t−j is the
average inflation rate in the last four quarters (i.e., the inflation over the
last year), and ī =
4 1 ∑ 3j=0
i t−j is the average interest rate over the same
period.
The equations are referred to as Phillips Curve (PC) and aggregate
demand (AD), respectively because the first one can be given a structural
interpretation as a PC while the second one may describe the transmission
of monetary policy on the economic activity quite like in an AD function.

Inflation Control in Central and Eastern European Countries 179
With this specification, agents extrapolate from the past inflation to formulate
the current period price level. The mechanism of transmission of
monetary policy to inflation is indirect: an expansionary monetary policy
takes place as a decrease in the real rate ī t−1 −¯π t−1 , which boosts the
economic activity in the AD equation; in the second moment, the pressure
on the demand enhances inflation, as illustrated in the PC equation.
The instrument and the mechanism of transmission of monetary policy are
then consistent with the operating procedures of both the FED and of the
Bundesbank, and later of the ECB.
Rudebush and Svensson (1999) allowed for an additional term β y2 y t−2
in the AD equation, but we found that, possibly also due to the smaller
dimension of our samples and the high collinearity with β y2 y t−2 , the contribution
of the two different effects in general could not be distinguished.
We, then considered the proposed AD equation sufficient, also because
one lag proved to be enough to have no serial correlation in the residuals.
Rudebush and Svensson also specified the model without intercepts α 0 ,β 0 ,
having formulated for mean-corrected data, but we preferred to allow for
the constant and test, for its possible exclusion explicitly.
Rudebush and Svensson (2002) remarked that ∑ 4
j=1 α πj = 1 can be
expected as it corresponds to a vertical PC in the long run. They also
explicitly discussed the fact that the backward looking formulation of
the PC and AD equations imply adaptive rather than rationale expectations,
but they argued that this may well be the case especially in a phase
of monetary and inflationary instability; as an alternative, they suggested
that the given specification may simply be considered as reduced form
equations.
Notice that even if the constraint ∑ 4
j=1 α πj = 1 is applied, the model
still does not necessarily impose a unit root to inflation, because the dynamics
of y t has to be taken into account too: consider for example α π1 = 1,
α π2 = α π3 = α π4 = 0, β y = 0, and the monetary policy rule ī t =¯π t + π t ;
the PC equation then becomes β r ∈ y, t+ ∈π, t, thus, inducing a stationary
behavior. It is indeed, precisely by steering the output gap using the interest
rate that the stabilization of inflation is ultimately possible.
This model may well be applied to the transition economies too, especially
considering that the accession of these countries to the EU requires
them to adopt a monetary policy setting that is institutionally compatible
with the one of the ECB. In the case of a small open economy, though,
two other factors should be taken into account: the demand of domestic
products generated by the trade partners and the effect of the international
competition on local prices.

180 Fabrizio Iacone and Renzo Orsi
Following Svensson (2000), we then augmented the model by introducing
the level of the economic activity in the international partners wt and the
percent real exchange rate depreciation (q t −q t−1 ), where q t = p ∗ t +e t −p t
is the logarithm of the real exchange rate and p t ,p ∗ t and e t are the logarithm
of the local and foreign level of prices and of the nominal exchange
rate, respectively. Both the variables are added to the AD equation, and
the real exchange rate is added to the PC equation as well. For the AD,
the assumption is that phases of high economic activity abroad result in
higher demand of locally produced goods, while a too high level of prices
(in real terms) causes a shift of the domestic and foreign demand towards
the external producers. The real exchange rate entered the PC equation,
because the international competition imposes some price discipline to the
local producers: for given foreign prices, a nominal exchange rate appreciation
makes foreign goods cheaper in local currency, thus, forcing the
domestic producers to lower their prices to keep up with the external competitors,
while for given nominal exchange rate higher foreign prices give
the domestic producers to set higher prices and stay in the market; we also
refer to Svensson (2000), where he explains how an increase in foreign
prices in local currency, either due to the move of the foreign price itself or
to the exchange rate, results in higher cost of inputs and then feeds back in
higher prices of output.
Maintaining the autoregressive structure of Rudebush and Svensson,
we describe the economy with the two equations model
π t = α 0 + α π1 π t−1 + α π2 π t−2 + α π3 π t−3
+ α π4 π t−4 + α y y t−1 − α q (q t−1 − q t−5 ) + ε π,t PC
y t = β 0 + β y y t−1 − β w w t−1 − β q (q t−1 − q t−5 ) + ε y,t AD
where we actually considered relevant for the exchange rate the depreciation
over the whole year.
In the original model, Svensson considered the real exchange rate rather
than the percent depreciation: in our model specification, we preferred the
latter because as we saw the real exchange rates of most of the CEECs
appreciated since the beginning of the transition without resulting in a
dramatic decline of the economic activity.
Moreover, we kept the AD/PC structure as a general reference, but
given that the specification is somewhat arbitrary, we tried to adapt it to
the economies considered. Our sample starts from 1990, and to avoid the
risk of model instability in the very first part of the sample, the data were
used only to compute the output gap or as lags. In some cases, we did

Inflation Control in Central and Eastern European Countries 181
not find adequate data so the sample period was even shorter. Data are
monthly, but in order to reduce the volatility, we used quarterly averages,
adjusting the frequency properly. We took the CPI to compute inflation and
the real exchange rate, and the seasonally adjusted industrial production
to derive a measure of economic activity (when only the nonseasonally
adjusted series was available, we run a preliminary step using the X-12
filter in EViews to remove seasonality); for the nominal interest rate we
used a three-months inter-bank rate or the Treasury bills rate of the same
maturity. More details on the data used are at the end of this paper. We
always considered Germany as the international reference, even if in the
first part of the sample period some countries pegged the exchange rate to
the US$: the EU in fact, constitutes by far the biggest trade partner for the
CEECs.
There is a strong seasonal component in the quarterly inflation, which
is likely to shift the weights towards the fourth lag in the PC equation;
the choice of the year appreciation of the real exchange rate was then also
convenient to remove the seasonal effect.
As a measure of the economic activity we took the output gap, defined
the difference between the observed and the potential output computed
using the Hodrik Prescott (HP) filter on the quarterly average of the production
index. Even if the HP gap is usually considered an inexact measure
of the economic cycle, due to its purely numerical definition, we still think
that it is at least informative of the effective output gap. Plots of the inflation
in the four countries are in Fig. 1 (figures are all collected at the end of
Figure 1.
Yearly inflation, Germany, Poland, Czech Republic, and Slovenia.

182 Fabrizio Iacone and Renzo Orsi
the work). The inflation used for this graph was defined as the growth rate
of prices on the previous year: we presented it albeit, we used a different
measure in our empirical study because it is very common in the descriptive
analysis in the literature. Clearly, though, averaging the inflation in this way
induces spurious autocorrelation in the data, so in the empirical analysis we
measure inflation as the annualized growth rate of prices over each period.
We plotted this and the output gap for Germany in Fig. 2; in Figs. 3–5,
we plot the same data and the yearly real exchange rate depreciation for
Poland, Czech Republic, and Slovenia, respectively. From these figures, it
Figure 2.
Quarterly inflation and output gap, Germany.
Figure 3.
Quarterly inflation, output gap, real exchange rate depreciation, Poland.

Inflation Control in Central and Eastern European Countries 183
Figure 4.
Republic.
Quarterly inflation, output gap, real exchange rate depreciation, Czech
Figure 5.
Slovenia.
Quarterly inflation, output gap, real exchange rate depreciation,
is already possible to notice that, while for Germany, the dynamics of inflation
is dictated by the output gap, in the three new EU members inflation
is largely dictated by the real exchange rate dynamics.
Estimation was carried out using OLS equation by equation, as in Rudebush
and Svensson (1999). We did not introduce any other modification to

184 Fabrizio Iacone and Renzo Orsi
the AD equation, but we re-wrote the PC as
π t = α 0 + ρ 0 π t−1 + ρ 1 π t−1 + ρ 2 π t−2 + ρ 3 π t−3 + ρ y y t−1
+ α q (q t−1 − q t−5 ) + ε π,t PC
(the term q t−1 − q t−5 does not appear in the equation for Germany). This
is a re-parametrization of the original equation, with
ρ 0 = (α π1 + α π2 + α π3 + α π4 − 1)
ρ 1 =−(α π2 + α π3 + α π4 ), ρ 2 =−(α π3 + α π4 ), ρ 3 =−α π4
Being simply a re-parametrization, the residual sum of squares that
has to be minimized is the same, so the OLS estimates are not different
than the estimates that one would obtain in the original model in levels.
The advantage of this specification is that long and short dynamics are
explicitly separated, ∑ 4
j=1 α πj = 1 corresponding to p 0 = 0, and that,
more importantly, the multi-collinearity due to the terms π t−1 to π t−4 is
much less severe.
Correct specification was primarily checked by looking at the tests for
normality (Jarque and Bera), autocorrelation (up to the fourth lag: Breusch
.Godfrey LM) and heteroskedasticity (white without cross terms) in the
residuals: we referred to these tests using N for the normality, AC for the
autocorrelation, and H for the heteroskedasticity. If the model appeared to
be correctly specified, we then analyzed the stability of the parameters over
time. If we did not reject the hypothesis of stability either, we moved to
test specific restrictions on the parameters, and to estimate a more efficient
version of the model. In all the tests, we used the conventional 5% size. In
the tables in the Appendix, we presented both the P-values associated to
the tests and a summary of the equation estimated when the restriction was
imposed.
We considered the normality test first, because we used its result to
choose between the small or large sample version of the other tests. Since
the small and large sample statistics are asymptotically equivalent in large
samples, the asymptotic interpretation of the results is not affected. Admittedly,
due to the asymptotic nature of the Jarque and Bera test, and to the
small sample lower order bias in the estimation of autoregressive coefficients,
the reader may be cautious in the interpretation of the results, especially,
when only portions of the dataset are used to estimate parameters
(like in the Chow stability test or in the estimates on sub-samples): notice
anyway that this is a problem that depends on the dimension of the sample;
so, indeed the same caveat applies to all the empirical analyzes present in

Inflation Control in Central and Eastern European Countries 185
the literature. The reader may then want to consider the estimates and the
statistics computed on the estimated parameters more as general indications
in small samples (especially, if the sub-sample 1998–2004 only is used),
but we think that despite these drawbacks, the estimates and the tests do
still provide some information on the structure that we intend to analyze,
albeit an approximate one.
Autocorrelation in the residuals is a serious mis-specification since it
results in inconsistent estimates given that both the equations include a
lagged dependent variable. Heteroskedasticity is a minor problem, because
estimation is simply inefficient (compared to the GLS estimator) but not
inconsistent. Yet, since the standard errors indicated by the regression are
not correct, evidence of heteroskedasticity requires at least a different estimation
of the variance-co-variance matrix of the estimates.
Due to the peculiarity of the transition, we think it is particularly important
to control the parameter stability over time, and possibly to model it
when apparent. We used as preliminary diagnostic the CUSUM squared
test, but also considered as a particular breakpoint in 1998, because of the
opening of the negotiation to access the EU. Clearly, this is just a broad
indication: one could also argue that by that time the negotiation opened
the transition to a market economy was already nearly complete, and the
issue was convergence to the EU standards. Yet, that period may still be
informative about a potential break even if it was not located exactly there.
We also considered country-specific breakpoints in the PC equations to
analyze the effect on the inflation dynamics of monetary regime changes:
for Germany, we allowed a break in 1999Q1, when the control of monetary
policy was transferred from the Bundesbank to the ECB, because it may
have been perceived as a weakening of the anti-inflationary stance, inducing
higher inflationary expectations; for Poland, we considered a break in
2000Q2, when the exchange rate commitment was formally abandoned;
for Slovenia, the change is in 2001Q1, when the approach towards the real
exchange rate became effective. We tested the presence of the break with a
standard Chow test, unless the sample after the break was very little, in this
case we used the Forecast test, which is exactly designed to test for breaks
when only a little data are located after the break.
If the model was correctly specified and stable, we improved the efficiency
of the estimates by removing the variables whose coefficients were
estimated with a sign opposite to the one prescribed in the economic theory
(we assumed that α y , α q , β y , β w , β q , β r are not negative), and by imposing
other restrictions (including ∑ 4
j=1 α πj = 1): we tested these with a Wald
statistic, and referred to these tests as W in the tables.

186 Fabrizio Iacone and Renzo Orsi
Of course, given the small dimension of the samples and the potential
instability of the models due to the transition, a certain caution should still
be exerted in the interpretation of the results. But, we think that even in
this case our analysis is at least able to get a general, broad picture of the
situation: the lack of precision that may be attributed to the small dimension
of the sample, for example, is already taken into account in the standard
error. If, under normality, a test statistic rejects the null hypothesis despite
the large variability due to the small sample, then we would still regard the
estimate as informative, although may be only on the sign.
3. The Empirical Evidence
3.1. Germany
As a benchmark case, we first estimated the model for Germany over the
period 1991Q1–2004Q1. The choice of the sample is two-fold: first, only
data after the German re-unification were considered, leaving many of the
problems related to that particular transition out of the discussion; second,
this time span is roughly the same one covered by the data of the CEECs in
most of the applied analyzes, making the results comparable in this sense.
We called this a “benchmark” model because it is widely assumed that this
transmission mechanism for monetary policy was at work in Germany in
the years we are interested in. Furthermore, Germany is geographically
and economically close to the CEECs, accounting for a large share of their
international trade. Finally, it is an interesting reference because Germany
is the biggest country in the euro-area: if the monetary transmission in the
CEECs works in a very different way, their integration in the euro may
adversely affect the dynamics of inflation.
The estimated model for Germany was
⎧
ŷ ⎪⎨ t = 0.011 + 0.769y t−1
(0.005) (0.084)
⎪⎩ ̂π t =−1.02π t−1
(0.10)
− 0.0038y t−1
(0.00163)
− 0.86π t−2
(0.12)
− 0.71π t−3 + 17.62y t−2
(0.10) (12.18)
over the period 1991Q2–2004Q1 for the AD, and 1993Q1–2004Q1 for
the PC.
According to the diagnostic tests, the AD equation was correctly specified
and stable over the whole sample; the CUSUMsq hit the boundary in
the period 1993–1996, but we found no evidence of break with the Chow

Inflation Control in Central and Eastern European Countries 187
test (further details about all the tests and a summary of the estimates are
in the tables at the end).
The inflation dynamics, on the other hand, was not stable when the
whole sample was taken into account. The instability, though was clearly
restricted to the first part of the sample, and could indeed be removed dropping
the years 1991 and 1992. It is interesting to observe that it is exactly
the period of the recovery of the inflationary shock due to the German
re-unification, a phenomenon that was usually regarded as temporary and
exceptional. Diagnostic tests confirmed that the equation estimated using
data from 1993 onwards was correctly specified and stable; notice anyway,
the distribution of the residuals did not appear to be normal, so the interpretation
of the other tests can only be justified asymptotically. Point estimates
of ρ 1 , ρ 2 , and ρ 3 were all very close to −1, suggesting a very high value of
α 4π , or a strong seasonal component in inflation; we also found that lagged
values of yt − 1 had a more significant effect, albeit even in this case the P-
value of the test H 0 : {αy = 0} vs. H 0 : {α y > 0} was between 5% and 10%.
Considering the model as a whole, anyway, we find these estimates
satisfactory, although not as much as those presented by Rudebush and
Svensson for the United States: we conjecture that the lower precision of
the estimates for Germany depended on the smaller number of observations
available.
3.2. Poland
Opposite to Germany, we consider Poland (and the other CEECs later)
as a country small enough to be affected by the international trade, so
we augmented the model with the real exchange rate depreciation with
respect to Germany and with the German output gap. Albeit our dataset
included 1993 too, we found that both the equations suffered from residual
autocorrelation, resulting in inconsistent estimates. We interpreted this as
evidence of instability, because when 1994 was taken as a starting point,
the residual autocorrelation was largely removed and the other diagnostic
tests were broadly compatible with a stable, correctly specified model. The
estimated model was
⎧
ŷ ⎪⎨ t = 0.020 + 0.467y t−1 − 0.0027y t−1
(0.008) (0.142) (0.001)
⎪⎩
̂π t =−0.64π t−1
(0.12)
− 0.67π t−2
(0.101)
− 0.51π t−3 + 21.46(q t−1 − q t−5 )
(0.10)
(7.88)
over the period 1994Q1–2004Q1 for the AD, and 1994Q1–2004Q1 for
the PC.

188 Fabrizio Iacone and Renzo Orsi
The variables referred to the trade partners were then not significant in
the AD equation: we found a certain effect at least for the real exchange rate
depreciation, and with a sign consistent with the macroeconomic theory,
but the realization of the t statistic was still rather below the critical value.
The absence of the two variables referring to the international trade could
be interpreted as a sign that Poland is still large enough to be more sensible
to the internal rather than to the international developments, but notice that
the situation was reversed for the PC equation, where only the external
conditions had a significant effect on the inflationary dynamics (again we
found that the effect of the omitted explanatory variable, y t−1 in this case,
had the sign predicted by the macroeconomic theory, but it failed to be
significantly different than 0).
We concluded performing a Forecast test for a break in 2000Q2 in
the PC equation, rejecting it (P-value 0.65). Since at that point, the Polish
national bank abandoned the exchange rate commitment and left the direct
inflation targeting to stand alone, it is fair to conclude that the change of
monetary target did not result in a destabilization of the inflation dynamics.
Since the target for monetary policy is defined mainly because it is assumed
that in that way the expected inflation can be favorably influenced, we prefer
not to give a structural interpretation of a backward looking formulation
of the inflation equation, but in this case we can at least conclude that the
change of target did not result in a worsening of the expectation of inflation.
Thus, it is likely that by 2000, the Polish central bank acquired sufficient
credibility to move away from a commitment that would have exposed it
to pressure from market speculation.
Although we summarized the diagnostic tests, concluding that the instability
that may be associated to the transition to a market economy can be
largely confined to the period before 1994, we also estimated a more restrictive
specification, in which the sample for the AD equation is from 1995
onwards, and for the PC from 1998 onwards. We considered this second
specification, because the residuals were not normally distributed, and an
asymptotic interpretation of the outcome of the autocorrelation test for the
AD equation was particularly dubious because the test statistic reached
approximately, the limit critical value, the P-value being slightly lower
than 0.05 (it was 0.046). As far as the PC equation, the Chow test did not
identify any break in 1998Q1 but the CUSUMsq statistic did indeed signal
a potential break in this year, albeit only mildly. The estimates in the more

estrictive model are
⎧
ŷ t = 0.021
⎪⎨
+ 0.454y t−1
(0.009)
⎪⎩
Inflation Control in Central and Eastern European Countries 189
(0.154)
̂π t =−0.57π t−1
(0.19)
− 0.0029y t−1
(0.001)
− 0.76π t−2
(0.13)
− 0.47π t−3 + 16.09(q t−1 − q t−5 )
(0.20)
(7.23)
over the period 1995Q1–2004Q1 for the AD, and 1998Q1–2004Q1 for
the PC, very similar then to the estimates on the longer sample. For the PC
equation, we also present the alternative specification
̂π t =−0.66π t−1
(0.20)
− 0.78π t−2
(0.13)
+ 19.22(q t−1 − q t−5 )
(7.46)
− 0.59π t−3 + 39.24π t−1
(0.20) (29.00)
estimated over the sample 1998Q1–2004Q1: the lagged output gap still
appeared in the determinants of the inflation dynamics, it had the correct
sign and it was also marginally significant with the 10% critical value and a
one-sided t test: a possible interpretation of this result could be that by 1998,
the PC equation evolved even closer to the standard textbook specification,
but we think that a longer dataset is needed to address this particular issue.
In any case, considering the whole model, we confidently conclude that
the Polish monetary authority was able to control inflation during these
years, but we think it mainly worked through the exchange rate management,
the evidence of the closed economy transmission mechanism, in fact,
being dubious.
3.3. Czech Republic
Czech Republic originated in 1993, from the split of the former Czechoslovakia.
Data availability is then slightly reduced, and it is also possible that
the division of the country acted as a source of instability additional to the
one generated to the transition. Although it is not possible to distinguish
between these two causes, the evidence of instability of the macroeconomic
structure was quite clear.
The sample for the estimation of theAD equation started in 1994Q4, but
we found that a break took place around 1999, according to the CUSUMsq
statistic. This is approximately also the point for which the Chow test is
to be computed, and we found strong evidence in favor of it (the P-value
associated to it was 0.01). Comparing the estimates in the two sub-samples,

190 Fabrizio Iacone and Renzo Orsi
the most relevant differences were in the fact that the coefficient of the real
rate, that signals the transmission of the monetary policy impulse from the
monetary authority to the economy, and the real exchange rate depreciation,
were only significant and with the correct sign in the second part of the
sample (the economic activity in Germany remained insignificant).
It is possible that instability affected the PC equation too, albeit in
this case the evidence was less compelling. Using the whole sample that
started in 1994, the CUSUMsq statistic did not indicate the presence of any
break, but according to the Chow test a discontinuity took place in 1998.
The estimated coefficient of the economic activity was largely insignificant,
despite having the same sign predicted by the economic theory, while we
found that the real exchange rate appreciation had a strongly significant
anti-inflationary effect. The estimated model was
⎧
ŷ ⎪⎨ t = 0.010 + 0.620y t−1
(0.006) (0.116)
⎪⎩ ̂π t =−0.76π t−1
(0.23)
− 0.03y t−1 − 0.083(q t−1 − q t−5 )
(0.001)
(0.050)
− 0.21π t−2
(0.25)
− 0.31π t−3 + 32.55(q t−1 − q t−5 )
(0.18)
(11.97)
over the period 1998Q1–2004Q1 for both the AD and the PC, while if we
relied on the CUSUMsq statistic rather than on the Chow one for the PC,
the PC equation estimated over the period 1994Q1–2004Q1 was
̂π t =−0.84π t−1
(0.15)
− 0.33π t−2
(0.17)
− 0.34π t−3 + 25.338(q t−1 − q t−5 )
(0.09)
(9.186)
Comparing these estimates, notice that if a break did indeed take place,
then the consequence was that the real exchange rate appreciation had a
stronger effect against inflation in the last part of the sample, that was
exactly when Czech central bank used inflation rather than exchange rate
targeting. As in the case of Poland, we then found no evidence that the
switch of monetary policy target resulted in a worsening of the inflationary
dynamics. On the contrary, if a change in the dynamics of the growth rate
of prices took place at all, when inflation targeting was introduced, it was
in favor of an easier control of it.
3.4. Slovenia
As we did for Czech Republic, in the case of Slovenia too we only considered
the part of the sample corresponding to the existence of an independent
state.

Inflation Control in Central and Eastern European Countries 191
The data available for the estimation started from 1994Q1 for the AD
equation and in 1993Q2 for the PC. We found anyway, evidence of model
mis-specification when the first year is included, resulting in residual autocorrelation
and inconsistent estimates: it is also fair to suspect, on the basis
of the CUSUMsq statistic, that a break took place in the first part of the
sample. We then removed 1993 from the dataset, and estimated the model
from 1994 onwards (sample period 1994Q1–2003Q3 for theAD, 1994Q1–
2003Q4 for the PC), obtaining
⎧
ŷ ⎪⎨ t = 0.0226 + 0.343w t−1
(0.167) (0.234)
⎪⎩
̂π t =−0.60π t−1
(0.14)
− 0.66π t−2
(0.12)
− 0.45π t−3 + 52.64(q t−1 − q t−5 )
(0.12)
(15.60)
The diagnostic tests confirmed that both the equations were correctly
specified and stable in the period considered, albeit, we acknowledge that
the estimates in the AD equation are only significant using a 10% threshold.
We are inclined to consider them anyway, suspecting that a more clear
link will emerge in the future, with a longer sample and an even higher
integration in the European economy. Notice, on the other hand, the absence
of the real interest rate, whose estimated coefficient even failed to have the
sign prescribed in the economic theory: this supported the argument of
Capriolo and Lavraac that, until recently, the interference of the central
bank on the financial markets made the interest rates not informative about
the monetary stance.
The estimated PC is qualitatively similar to the Polish and Czech one,
with inflation only driven by the exchange rate dynamics but not by the
output gap: indeed, ˆβ y even resulted as negative, so in the final specification
we excluded y t−1 from the explanatory variables altogether. In order to see,
if the more active exchange rate policy resulted in an easier inflation control
and then in a larger β q , we also tested (with a Forecast test) for a break in
2001, but we did not reject the hypothesis of stability.
3.5. Some Concluding Remarks
Poland, Czech Republic, and Slovenia are small economies that in a few
years re-shaped their productive and distributive structures, opened to the
international trade, established a functioning market economy and joined
the EU. Despite these common features, they differ quite remarkably for
the time and the condition, in which they started the transition to the market
economy, for the policies they implemented since 1989, and for the size

192 Fabrizio Iacone and Renzo Orsi
and the relative importance of the trade with the rest of the EU. It is then
fair to expect that both the similarities and the differences emerge, and this
is indeed the case.
The most relevant common feature is the presence of a certain instability
in the first part of the sample. To appreciate the importance of the transition,
we observed that, according to a study of Coricelli and Jasbec (2004), the
characteristics that may be associated to the initial conditions were the main
driving forces of the real exchange rate dynamics. The variables that were
more directly related to the economic notions of supply and demand, only
acquired importance after a period of approximately five years. We found
that the macroeconomic model structure begun to show a stable pattern
only from 1994 onward, confirming the findings of Coricelli and Jasbec.
Even taking 1994 as a starting value, anyway, some elements of instability
remained, especially with respect to Czech Republic.
The instability of the estimated macroeconomic relations is also informative
about the speed of the transition. In this respect, we found that in
Slovenia the adverse effect of theYugoslavian civil war canceled the advantage
due to the self-management reform; Czech Republic, which had to face
not only the decentralization and the break-up of CMEA but even the split
of Czechoslovakia, fared worse.
The relation between the variables got closer to the standard textbook
description of a market supply and demand structure in the last few years.
Yet, even in that part of the sample evidence of a transmission mechanism
of monetary policy based on the interest rates was only present for
Poland, and that too turned out to be very weak. Although it is not surprising
that the exchange rate has a prominent role in inflation control in small
open economies, our findings cannot be explained simply by this argument,
because we explicitly include the exchange rate in both the equations of
the model, then taking it into account (and holding it fixed in the interpretation
of the results) in the multiple regression framework. One has rather
to conclude that the interest rate channel of transmission of monetary policy
was weak or obstructed, as indeed explicitly argued for Slovenia. This
also means that, although these economies were acknowledged as functioning
market economies, they may still be lagging behind; nonetheless,
since a good development took place during the accession period, it is fair
to expect that participation to the EU will foster integration. Meanwhile,
their presence should not hamper inflation control too much, because the
exchange rate is clearly a valid instrument for that purpose: this means that
in a widened euro-zone, the Eurosystem may control inflation in the CEECs
by controlling it in the core area.

Inflation Control in Central and Eastern European Countries 193
Although they are all small open economies, a pattern can be envisaged
in terms of dimension and openness to international trade, and this
is reflected in the estimated models: Poland, is the only country in which
the international factors did not affect the AD. Another way to appreciate
the importance of the international openness is to look at the estimated
effect of a 1% appreciation of the exchange rate: the impact on the inflation
dynamics is clearly ranked according to the relative dimension of trade.
Stability analysis is also important because it allows us to understand if
the switch in Poland and in Czech Republic from exchange rate to inflation
targeting affected the price setting formation. We did not find any evidence
of it, nor we found that a more aggressive exchange rate policy in Slovenia
eased the costs of disinflation from 2001 onwards. The instability that we
found for Czech Republic seems to suggest an evolution of the macroeconomic
structure towards a market economy, and should then have more to
do with EU accession than with inflation targeting. One main implication
that we perceive is that the exchange rate commitment is either irrelevant
or, more likely, replaceable with inflation targeting as a nominal anchor.
We think that this conclusion is of particular interest to help choosing the
monetary target for the period preceding the last two years before fixing
the exchange rate in the ERM2: inflation targeting should be preferred and
ERM2 membership should only be limited to the two mandatory years.
We also think that this lesson can be extended to other emerging market
economies, and that inflation targeting, rather than explicit exchange rate
commitment, should be preferred, especially if strict capital controls are
not in place.
References
Amato, JD and S Gerlach (2002). Inflation targeting in emerging market and transition
economies: lessons after a decade. European Economic Review 46, 781–790.
Capriolo, G and V Lavrac (2003). Monetary and exchange rate policy in Slovenia. Eastward
Enlargement of the Euro-Zone Working Papers, 17G. Berlin: Free University Berlin,
Jean Monnet Centre of Excellence, 1–35.
Coricelli, F and B Jasbec (2004). Real exchange rate dynamics in transition economies.
Structural Change and Economic Dynamics 15, 83–100.
Dvorsky, S (2000). Measuring central bank independence in selected transition countries
and the disinflation process. Bank of Finland, Bofit Discussion Paper 13. Helsinki:
Bank of Finland, 1–14.
Iacone, F and R Orsi (2004). Exchange rate regimes and monetary policy strategies for
accession countries. In Fiscal, Monetary and Exchange Rate Issues of the Eurozone
Enlargement, K Zukrowska, R Orsi and V Lavrac (eds.), pp. 89–136. Warsaw: Warsaw
School of Economics.
Maliszewski, WS (2000). Central bank independence in transition economies. Economics
of Transition 8, 749–789.

194 Fabrizio Iacone and Renzo Orsi
Rudebush, GD and LEO Svensson (1999). Policy rules for inflation targeting. In Monetary
Policy Rules, John B Taylor (ed.), pp. 203–246. Chicago: Chicago University Press.
Rudebush, GD and LEO Svensson (2002). Eurosystem monetary targeting: lessons from
U.S. data. European Economic Review 46, 417–442.
Svensson, LEO (2000). Open-economy inflation targeting. Journal of International Economics
50, 155–183.
Appendix A
Summary of the Results
Note to the Tables: for each equation, N indicates the normality test, AC
is the LM test of no autoregressive structure in the residuals and H is the
test for the heteroskedasticity; W indicates the test of those restrictions
that reduce the corresponding equation as specified in general to the one
specifically used. For each test, we report the P-value: the small sample
version of the test is taken, unless normality is rejected. When the estimated
equation is restricted, the test statistics N, AC, H, Chow, W are calculated
in the unrestricted model.
Table 1a.
Germany.
AD
[sample: 91Q2–04Q1]
ŷ t = 0.011 + 0.769 yt −1 − 0.038r t−1
[N: 0.38] [AC: 0.20] [H: 0.17]
PC
[sample: 93Q1–04Q1]
ˆπ t =−1.02π t−1 − 0.86π t−2 − 0.71π t−3 + 17.62y t−2
[N: 0.00] [AC: 0.24] [H: 0.10] [Chow: 0.18] [W: 0.44]

Inflation Control in Central and Eastern European Countries 195
Table 2a.
Poland, 1994 onwards.
AD
[sample: 94Q1–04Q1]
ŷ t = 0.020 + 0.467y t−1 − 0.0027r t−1
[N: 0.00] [AC: 0.047] [H: 0.49] [Chow: 0.046] [W: 0.57]
PC
[sample: 94Q1–04Q1]
ˆπ =−0.64π t−1 − 0.67π t−2 − 0.51π t−3 + 21.46(q t−1 − q t−5 )
[N: 0.00] [AC: 0.056] [H: 0.29] [Chow: 0.36] [W: 0.06] [Chow: 2000Q2: 0.65]
Table 2b.
Poland, restricted sample.
AD
[sample: 95Q1–04Q1]
ŷ t = 0.021 + 0.454y t−1 − 0.0029r t−1
[N: 0.00] [AC: 0.07] [H: 0.54] [Chow: 0.54] [W: 0.64]
PC
[sample: 94Q1–04Q1]
ˆπ t =−0.57π t−1 − 0.76π t−2 − 0.47π t−3 + 16.09(q t−1 − q t−5 )
[N: 0.57] [AC: 0.25] [H: 0.79] [W: 0.39]

196 Fabrizio Iacone and Renzo Orsi
Table 3.
Czech Republic, restricted sample.
AD
[sample: 98Q1–04Q1]
ŷ t = 0.010 t−1 − 0.03r t−1 + 0.083(q t−1 − q t−5 )
(0.006) (0.116) (0.001)
(0.050)
[N: 0.79] [AC: 0.07] [H: 0.54] [W: 0.15]
PC
[sample: 98Q1–04Q1]
ˆπ t =−0.76π t−1 − 0.21π t−2 − 0.31π t−3 + 32.55(q t−1 − q t−5 )
[N: 0.71] [AC: 0.34] [H: 0.33] [W: 0.26]
Table 4.
Slovenia.
AD
[sample: 94Q1–03Q3]
ŷ t = 0.226y t−1 + 0.343w t−1
(0.167) (0.234)
[N: 0.30] [AC: 0.37] [H: 0.86] [Chow 0.31] [W: 0.31]
PC
[sample: 94Q1–03Q4]
ˆπ t =−0.60π t−1 − 0.66π t−2 − 0.45π t−3 + 52.64(q t−1 − q t−5 )
[N: 0.44] [AC: 0.35] [H: 0.65] [Chow: 0.83] [W: 0.15] [Break 2001Q1:0.69]

Inflation Control in Central and Eastern European Countries 197
Datastream codes.
Czech
Germany Poland Republic Slovenia
Exchange rate USXRUSD
(US$ per ∈)
Exchange rate BDESXUSD. POI..AF. CZXRUSD. SJXRUSD.
(vs. US$)
CPI BDCONPRCF POCONPRCF CZCONPRCF SJCONPRCF
Industrial BDINPRODG POIPTOT5H CZIPTOT.H SJIPTO01H
production
3-month-rate BDINTER3 PO160C.. CZ160C.. SJI60B..
Diagnostic tests of some specifications that we dismissed:
Table 5b.
Germany, PC equation, whole dataset.
PC
[sample: 91Q3–04Q1]
ˆπ t = 0.47 − 0.29π t−1 − 0.66π t−1 − 0.53π t−2
(0.48) (0.18) (0.18) (0.17)
[N:0.00] [AC: 0.20] [H: 0.06] [Chow: 0.62]
− 0.50π t−3 .
(0.18)
+ 7.22y t−1
(13.41)

198 Fabrizio Iacone and Renzo Orsi
Table 5c.
Poland, whole dataset.
AD
ŷ t = 0.02 + 0.509y t−1 − 0.0025r t−1
(0.009) (0.166) (0.001)
[N: 0.00] [AC: 0.20] [H:0.53] [Chow: 0.06]
PC
ˆπ t =−0.42 − 0.10π t−1
(1.25)
(0.08)
− 0.130w t−1
(0.203)
− 0.77π t−1 − 0.78π t−2
(0.12) (0.11)
− 0.67π t−3 . + 22.55y t−1
(0.10) (27.42)
[N: 0.00] [AC: 0.01] [H: 0.07] [Chow: 0.81]
+ 18.08(q t−1 − q t−5 )
(9.29)
[sample: 93Q2–04Q1]
− 0.054(q t−1 + q t−5 )
(0.045)
[sample: 93Q2–04Q1]

Inflation Control in Central and Eastern European Countries 199
Table 5d.
Czech Republic, whole dataset.
AD
ŷ t = 0.007 + 0.617y t−1 − 0.0001r t−1
(0.005) (0.140) (0.001)
[N: 0.44] [AC: 0.94] [H: 0.06] [Chow: 0.01]
PC
ˆπ t = 2.45 − 0.24π t−1
(1.17)
(0.19)
− 0.186w t−1
(0.229)
− 0.68π t−1 − 0.28π t−2
(0.21) (0.19)
+33.22(q t−1 − q t−5 )
− 0.36π t−3 +22.10y t−1
(0.10) (24.4)
[N: 0.00] [AC: 0.25] [H: 0.086 [Chow: 0.01]
[sample: 93Q4–04Q1]
+ 0.047(q t−1 + q t−5 )
(0.063)
[sample: 94Q1–04Q1]
[W:0.19]

200 Fabrizio Iacone and Renzo Orsi
Table 5e.
Slovenia, PC equation, whole dataset.
PC
ˆπ t = 4.71 − 0.50π t−1
(1.41)
(0.19)
− 0.03π t−1 − 0.40π t−2
(0.11) (0.11)
[sample: 93Q2–03Q4]
− 0.10π t−3 . + 2.45y t−1 + 48.28(q t−1 − q t−5 )
(0.07) (26.70)
(17.73)
[N: 0.84] [AC: 0.03] [H: 0.02] [Chow: 0.71]

Topic 2
Credit and Income: Co-Integration Dynamics
of the US Economy
Athanasios Athanasenas
Institute of Technology and Education, Greece
1. Introduction
In this study, I seek to identify the existence of a significant statistical relationship
between credit (as commercial bank lending) and income (GDP),
for the US post-war economy, in terms of a contemporary co-integration
methodology.
The main empirical finding regarding the hypothesis that causality, in
the long run, is directed from credit to income, agrees with the “credit-view”.
This can be verified by the the post-war US data. In this chapter, I have
identified a dynamic causality effect in the short run, from income changes
to credit ones. To obtain the results cited here, I have applied a co-integration
analysis. In addition to considering the formulated VAR, I place particular
emphasis upon the stability analysis of the estimated equivalent first-order
dynamic system. Finally, dynamic forecasts from the corresponding error
correction variance (ECVAR) are obtained, in order to verify the validity
of the co-integration vector used.
This study have four sections. Section 2 reviews, in a brief note,
the literature on credit and income growth of the post-war US economy.
Section 3 deals with methodological issues concerning the contemporary
co-integration analysis and the data used. Section 4 presents the econometric
analysis and the empirical results; while Section 5 concludes the
credit-income causality issue, placing emphasis on the stability analysis
of the obtained first-order dynamic system and the forecasts from the
corresponding ECVAR.
201

202 Athanasios Athanasenas
2. The Credit Issue Researched: A Brief Note
on the US Economy
There is an evidence that money tends to “lead” income in a historical sense
(see Friedman and Schwartz (1963) and Friedman (1961; 1964). Where the
mainstream monetarists through the “quantity theory” explain the empirical
observations as the causal relationship running from money to income.
Since the seminal works of Sims, empirical validation of the relationship
between money and income fluctuations has been established (Sims, 1972;
1980a). Since the publication of the works of Goldsmith (1969), Mckinnon
(1973), and Shaw (1973), the debate has been going on about the role of
financial intermediaries and bank credit in promoting the long-run growth.
On the basis of historical data, Friedman and Schwartz (1963) argue that
major depressions of the US economy have been caused by autonomous
movements in money stock. 1 Sims (1980a) concludes that on one hand,
money stock emerges as causally prior accounting for a substantial fraction
of income variance during the inter-war and post-war periods of the business
cycles. On the other hand, old skepticism remains on the direction of
causality between money and income.
It is well known that traditional monetarists are consistent with the
old-classic view that only “money matters”, so that even when tightening
of bank credits does occur during recessions, they see these as part
of the endogenous financial system, rather than exogenous events, which
induce recessions. As Brunner and Meltzer (1988) argue, banking crises
are endogenous financial forces, which directly affect business cycles conditional
upon the monetary propagation mechanism. 2
In contrast, the “new-credit” viewers stress further the importance of
credit restrictions, while accepting the fundamental inefficiencies of the
monetary policy. 3 Bernanke and Blinder (1988), in their seminal article,
conclude that credit demand is becoming relatively more stable than money
1 Ibid.
2 Note that monetarists seem to stress mainly, the complementarity of credit and money
channels of transmission, the short-run stability of the money multiplier, and the long-run
neutrality of money.
3 The “new-credit” view combines the “old-credit” view of the money to spend perspective,
with the money to hold perspective of the money view. The “old-credit” view focused on
decisions to create and spend money, on the expansion effects of bank lending, and emphasized
the issue of the non-neutrality of credit money in the long-run (see also, Trautwein,
2000).

Credit and Income 203
demand since 1979 and throughout the 1980s, where, money demand
shocks became much more important relative to credit demand shocks in
the 1980s, supported by their estimation of greater variance of money.
Evidently, one of the most challenging issues of the applied monetary
theory is the existence and importance of the credit channel in the monetary
transmission mechanism. Bernanke (1988) emphasizes that according to the
proponents of the credit view, bank credit (loans) deserve special treatment
due to the qualitative difference between a borrower going to the bank for
a loan and a borrower raising funds by going to the financial markets and
issuing stock or floating bonds. 4
Kashyap and Stein (1994) leave no doubt while supporting Bernanke’s
(1983), and Bernanke’s and James’s (1991) examination of the Great
Depression in the United States, that the conventional explanation for the
depth and persistence of the Depression is one of the strongest pieces of evidence
supporting the view that shifts in loan supply can be quite important.
The supporting evidence stands strong, considering also that the decline of
intensity as seen in recessions are partially due to a cut-off in bank lending
(Kashyap et al., 1994). 5
King and Levine (1993) stress that financial indicators, such as the
importance of the banks relative to the central bank, the percentage of
credit allocated to private firms and the ratio of credit issued to private
firms to GDP, are strongly related with growth. For the relevant role of the
monetary process and the financial sector, see, in particular, (Angeloni et al.,
2003; Bernanke and Blinder, 1992; Murdock and Stiglitz, 1993; Stock and
Watson, 1989; Swanson, 1998).
More recently, Kashyap and Stein (2000) proved that the impact of
monetary policy on lending behavior is stronger for the banks with less
liquid balance sheets, where liquidity is measured by the ratio of securities
4 Stiglitz (1992) stresses the fact that the distinctive nature of the mechanisms by which
credit is allocated plays a central role in the allocation process. He identifies several crucial
reasons that banks are likely to reduce lending activity (p. 293), as the economy goes into
recession, where banks’ unwillingness and the inability to make loans obviates the effect
of monetary policy. Bernanke and Blinder (1992) find that the transmission of monetary
policy works through bank loans, as well as through bank deposits. Tight monetary policy
reduces deposits and over time banks respond to tightened money by terminating old loans
and refusing to make new ones. Reduction of bank loans for credit can depress the economy.
5 Both Bernanke and Blinder (1992) and Gertler and Gilchrist (1993) using innovations in
the federal funds rate as an indicator of monetary policy disturbances, find that M1 or M2
declines immediately, while bank loans are slower to fall, moving contemporaneously with
output.

204 Athanasios Athanasenas
to assets. Their principal conclusions can be narrowed down to: (a) the existence
of the credit-lending channel of monetary transmission, at least for the
United States is undeniable and (b) the precise quantification and accurate
measurement of the aggregate loan-supply consequences of monetary policy
remain very difficult in econometrics due to the large estimation biases.
See also the works of Mishkin (1995), Bernanke and Gertler (1995), and
Meltzer (1995), for the bank-lending channel. Lown and Morgan (2006)
stress further the substantial issue of the role of fluctuations in commercial
credit standards and credit cycles being correlated with real output.
All previous works provide a clear evidence that is consistent with
the existence of a credit-lending channel of monetary transmission. The
very heart of the credit-lending view is the proposition that the Central
Banks, in general, and the Federal Reserve in the United States, in particular,
can shift banks’ loan supply schedules, by conducting open-market
operations. 6
Consequently, given the afore-mentioned empirical research on the
credit-lending channel and the established relationship between financial
intermediation and economic growth in general, our main focus here is to
analyze in detail the causal relationship between finance and growth by
focusing on bank credit and income GNP, in the post-war US economy.
Analyzing in detail here means placing particular emphasis: (a) on a contemporary
co-integration approach, and (b) on the stability analysis of the
observed first-order dynamic system and the dynamic forecasts from the
corresponding ECVAR.
3. Methodological Issues and Data
In the empirical analysis, for the case of the US post-war period 1957–2007,
we test for the existence of causality between the total loans and leases at
commercial banks, denoted by real credit, representing the development of
the banking sector, and the money income, GNP, denoted by real income,
representing national economic performance. Both the variables are quarterly
seasonally adjusted from 1957:3 to 2007:3, i.e., 201 observations, and
are expressed in real terms, indexed by 1982–1984 as base 100, in billions of
US$. Considering the natural logs, I define two new variables (W i ,Y i ) such
that Y i = ln(real income i ) and W i = ln(real credit i ), for i = 1, 2,...,201.
6 It is noted that the credit-lending channel also requires an imperfect price adjustment and
that some borrowers cannot find perfect substitutes for bank loans.

Credit and Income 205
My data is obtained on line from the Federal Reserve Bank of Saint Louis,
Missouri, through their open source database. 7
Researchers usually employ some measure of the stock of money over
GNP, as a proxy for the size of the “financial depth” (see for instance,
Goldsmith, 1969; Mckinnon, 1973). This type of financial indicator does
not inform us as to whether the liabilities are those of the central banks,
commercial banks, or other financial intermediaries. In this way, the creditchannel
issue cannot be analyzed, and the significant role of credit cannot
be isolated. Moreover, this type of financial indicator is mainly applicable
to the developing countries, since the financing of the economy is to a
great extent carried out by the public sector and controlled mainly by its
central bank.
An advanced economy such as the United States, with a fully liberalized
banking and financial system, provides an excellent case for testing the
modern credit view such that the commercial bank credit itself has to be
modeled as a fundamental, financial, and an independent monetary variable
that affects money income, and hence the economic performance, in the
long run.
Based on the cited references, we would accept the value of commercial
bank credit to the private sector, as a measure of the ability of the banking
system to provide finance-led income growth. The extent to which money
income growth is associated with the credit provision from the financial
sector is examined through the use of contemporary co-integration methods
and system stability analysis.
Initially, the order of integration of the two variables is investigated
using standard unit root tests (Dickey and Fuller, 1979; Harris, 1995). The
next step is the computation of co-integration vectors by applying the maximum
likelihood (ML) approach considering the error-correction representation
of the VAR model (Harris, 1995; Johansen and Juselius, 1990). We
transformed the initial VAR to an equivalent first-order dynamic system
to perform the proper stability analysis, which revealed that the system
under consideration is stable. It should be re-called that stability is of vital
importance for obtaining consistent forecasts, and this issue is stressed
appropriately in Sections 4 (4.2 and 4.6) and 5.
I proceed with the utilization of the vector error-correction modeling
following Engle and Granger (1987), and testing for the short-run dynamic
relationship on causality effects between money and income.
7 And, we are deeply thankful for this.

206 Athanasios Athanasenas
I end up by applying a dynamic forecasting technique with the estimated
ECVAR. The very low value of Theil’s inequality coefficient U, provides
a concrete evidence that I have formulated the suitable ECVAR obtaining,
thus, robust results. Our particular emphasis on the system stability is
evident and it is clarified in detail in the following section.
4. Co-Integration
Considering the series {Y i }, {W i } and applying the Dickey–Fuller
(DA/ADF) tests (Dickey and Fuller, 1979; 1981; Harris, 1995, pp. 28–47),
I found that both series are not stationary, but they are integrated of order
1, that is I(1). This implies that by differentiating the initial series, we
get stationary ones. In other words, the series Y i = Y i − Y i−1 and
W i = W i − W i−1 are stationary, that is I(0). This can be easily verified
from Fig. 1, where the non-stationary series {Y i }, {W i } are also presented.
Y i
W i
∆Y i
∆W i
Figure 1. The I(1) series {Y i }, {W i } and the stationary ones {Y i }, {W i }.

Credit and Income 207
Since the variables Y i , W i are used in this study, it should be re-called that
the parameters of a long-run relationship represent constant elasticities.
It should be re-called that if two series are not stationary but they have
common trends so that there exist a linear combination of these series that
is stationary, which means that they are integrated in a similar way and for
this reason, they are called co-integrated, in the sense that one or the other
of these variables will tend to adjust so as to restore a long-run equilibrium.
Also, if there is a linear trend in the data, as in the case of Y i and W i as
shown in Fig. 1, then we specify a model including a time-trend variable,
allowing thus the non-stationary relationships to drift.
4.1. The VAR Model and The Equivalent ECVAR
We start this section by formulating and estimating an unrestricted VAR of
the form:
p∑
x i = δ + µt i + A j x i−j + w i (1)
j=1
where x ∈ E n (here E denotes the Euclidean space), δ is the vector of
constant terms, t i is a time-trend variable, µ is the vector of corresponding
coefficients, and w is the noise vector. The matrices of coefficients A j , are
defined on E n × E n . It is noted that variable t i is included for the reason
mentioned above. It can be easily shown (Johansen, 1995), that (1) may be
expressed in the form of an equivalent ECVAR, that is:
p−1
∑
x i = δ + µt i + Q j x i−j + x i−1 + w i (2)
j=1
where Q j = ( ∑ j
k=1 A k − I).
After estimation, we may compute matrix from:
⎛ ⎞
p∑
= ⎝ A j
⎠ − I
j=1
(2a)
or, directly from the corresponding ECVAR as given in Eq. (2). It is re-called
that this type of VAR models like the one presented above, is recommended
by Sims (1980a; b), as a way to estimate the dynamic relationships among
jointly endogenous variables. It should be noted that for the case under

208 Athanasios Athanasenas
consideration, vector x in Eqs. (1) and (2) is 2-dimensional, i.e.,
[ ]
Yi
x i = and it is x ∼ I(1).
W i
It is known that the matrix can be decomposed such that = AC,
where the elements of A are the coefficients of adjustment and the rows
of matrix C are the (possible) co-integrating vectors. In some books, A is
denoted by α and B by β ′ , although capital letters are used for matrices.
Besides, β denotes the coefficient vector in a general linear econometric
model. To avoid any confusion, we adopted the notation used here, as well
as in Mouza and Paschaloudis (2007).
Usually, matrices A and C are obtained by applying the ML method
(Harris, 1995; Johansen and Juselius, 1990, p. 78). According to this procedure,
a constant and/or trend can be included in the co-integrating vectors
in the following way.
Considering Eq. (2), we can augment matrix to accommodate, as an
additional column, the vectors δ and µ in the following way.
˜ = [.µδ]. (3)
In this case, ˜ is defined on E n × E m , with m>n. For conformability,
the vector x i−1 in Eq. (2) should be augmented accordingly by using the
linear advance operator L (such that L k y i = y i+k ), i.e.,
⎡
˜x i−1 = ⎣ x ⎤
i−1
Lt i−1
⎦ .
(3a)
1
Hence, Eq. (2) takes the form:
p−1
∑
x i = Q j x i−j + ˜˜x i−1 + w i . (4)
j=1
Note that no constants (vector δ), as well as coefficients of the time trend
(vector µ) are explicitly presented in the ECVAR in Eq. (4), which specifies
precisely a relevant set of n ECM.
It is assumed at this point that matrices C and A refer to matrix ˜ as
seen in Eq. (4). Let us consider now the kth row of matrix C, that is c ′ k. .8 If
this row is assumed to be a co-integration vector, then the (disequilibrium)
8 Note that dot is necessary to distinguish the kth row of C, i.e., c ′ k. , from the transposed of
the kth column of this matrix that is c ′ k .

Credit and Income 209
errors computed from u i = c ′ k. ˜x i must be a stationary series. Considering
now the kth column of matrix A, that is a k , and given that u i−1 = c ′ k. x i−1,
then the ECVAR in Eq. (4) can be written as:
p−1
∑
x i = Q j x i−j + a k u i−1 + w i . (5)
j=1
This is the conventional form of an ECVAR, when matrix ˜ instead
of is considered. In any case, the maximum lag in Eq. (5) is p − 1. It
should be noted that this specification of an ECM is fully justified from the
theoretical point of view. However, if we want to include an intercept in
Eq. (5), i.e., in the short-run model, it may be assumed that the intercept in
the co-integration vector is cancelled by the intercept in the short-run model,
leaving only an intercept in Eq. (5). Thus, when a vector of constants is to
be included in Eq. (4), which, in this case, takes the form:
p−1
∑
x i = δ + Q j x i−j + ˜˜x i−1 + w i (6)
j=1
then Eq. (5), matrix ˜ and the augmented vector ˜x will become:
p−1
∑
x i = δ + Q j x i−j + a k u i−1 + w i
j=1
(6a)
˜ = [.µ]
(6b)
[ ]
xi−1
˜x i−1 = . (6c)
Lt i−1
According to Eq. (6a), the co-integrating vector c ′ k.
, used to compute
u i = c ′ k. ˜x i, includes only the coefficient of the time-trend variable. The
inclusion of a trend in the model can be justified, if we examine the estimation
results of a long-run relationship considering Y and W. In such a
case, we immediately realize that a trend should be present.
After adopting the VAR as seen in Eq. (1), the next step is to determine
the value of p from Table 1 (Holden and Perman, p. 108).
We see from Table 1 that for α ≤ 0.05, p = 4, which means that we
have to estimate a VAR(4), with only one deterministic terms (i.e., trend).
After estimation, we found that matrix ˜ (hat is omitted for simplicity),

210 Athanasios Athanasenas
Table 1. Determination of the value of p.
Lag length p
LR
Value of p (probability)
1 — —
2 132.91 0.0000
3 14.988 0.0047
4 14.074 0.0071
5 2.7328 0.6035
6 5.1465 0.2726
7 2.3439 0.6728
8 5.2137 0.2661
specified in Eq. (6b) has the following form:
[ Y i W i t i ]
−0.092971 0.028736 0.000320
˜ =
. (7)
0.016209 −0.024594 0.000124
4.2. Dynamic System Stability
TheVAR(4) can be transformed to an equivalent first-order dynamic system,
in the following way.
⎡ ⎤ ⎡
⎤ ⎡ ⎤
x i A 1 A 2 A 3 A 4 x i−1
⎢ Lx i
⎣ L 2 ⎥
x i
⎦ = ⎢ I 2 0 0 0
⎥ ⎢ Lx i−1
⎣ 0 I 2 0 0 ⎦ ⎣ L 2 ⎥
x i−1
⎦
L 3 x i 0 0 I 2 0 L 3 x i−1
⎡ ⎤ ⎡ ⎤ ⎡ ⎤
δ µ w i
+ ⎢ 0
⎥
⎣ 0 ⎦ + ⎢ 0
⎥
⎣ 0 ⎦ t i + ⎢ 0
⎥
⎣ 0 ⎦ . (8)
0 0 0
L in this place, denotes the linear lag operator, such that L k z i = z i−k .
Equation (8) can be written in a compact form as:
y i = Ãy i−1 + d + zt i + v i
(8a)
where
y i ′ = [x i Lx i L 2 x i L 3 x i ], d ′ = [δ 0 0 0],
z ′ = [µ 0 0 0], v i ′ = [w i 0 0 0]
and the dimension of matrix à is (8 × 8).

Credit and Income 211
Table 2.
Eigen values.
No. Real part Coefficient of imaginary part Length
1 0.94 0 0.94
2 0.8567 0.0579 0.8586
3 0.8567 −0.0579 0.8586
4 0.3807 0.0 0.3807
5 0.0367 0.3655 0.3674
6 0.0367 −0.3677 0.3674
7 −0.3581 0.0 0.3581
8 −0.1142 0.0 0.1142
To decide whether the dynamic system described by Eq. (8a) is stable, we
compute the eigenvalues of matrix Ã, presented in Table 2.
Since the greater length (0.94) is less then 1, the dynamic system as
given in Eq. (8a) is stable and can be used for forecasting purposes. A side
verification of this stability test, is that once the system is stable, then the
elements of the state vector x in the initial VAR(4), which in this case are the
series {Y i }, {W i }, are either difference stationary series (DSS), or in some
cases, stationary series. In fact, we show that these series are DSS and in
particular, they are I(1).
4.3. The Estimated Co-Integrating Vectors
We applied the ML method, to compute matrices C and A, which have the
following form:
Y W t
[ ]
1 −0.289613 −0.003621
C =
,
1 −0.653108 −0.000292
[ ]
−0.087991 −0.004980
A =
−0.038535 0.054745
(9)
satisfying AC = ˜. We can easily verify that only the first row of matrix
C is a promising candidate, verified from the computed value of the t-
statistic (−0.23), which corresponds to the (1, 2) element of matrix A, that
corresponds to the second row of matrix C. Thus, we have the co-integrating

212 Athanasios Athanasenas
vector:
[1 − 0.289613 − 0.003621] (10)
producing the errors u i , which are the disequilibrium errors obtained from:
u i = Y i − 0.289613W i − 0.003621t i .
(10a)
It should be noted that the vector specified in Eq. (10) is a co-integration
vector, iff the series {u i } computed from Eq. (10a) is stationary. To find out
that this series is stationary, we run the following regression with a constant
term, since ∑ u i ̸= 0.
q∑
u i = a + b 1 u i−1 + b j+1 u i−j + ε i . (11)
Note that the value of q is set such that the noises ε i to be white. With q = 3,
the estimation results are as follows:
3∑
u i = 0.4275 − 0.07384 u i−1 + ˆb j+1 u i−j +ˆε i
(0.1174) (0.02029) (11a)
j=1
t =−3.64.
It should be noted that in Eq. (11a), there is no problem regarding
autocorrelation and heteroscedasticity. We have to compute the t u -statistic
from MacKinnon (1991, pp. 267–276) critical values (see also Granger and
Newbold, 1974; Hamilton, 1994; Harris, 1995, Table A6, p. 158; Harris,
1995, pp. 54–55). This statistic (t u = ∞ + 1 /T + 2 /T 2 , where T
denotes the sample size) is evaluated from the relevant table, taking into
account Eqs. (10a) and (11a). Note that in the latter equation, there is only
one deterministic term (constant). The value of the t u -statistic for this case
is −3.3676 (α = 0.05). Hence, since −3.64 < −3.3676, we reject the
null that the series {u i } is not stationary. Recall that the null [u i ∼ I(1)] is
rejected in favor of H 1 [u i ∼ I(0)], if t

Credit and Income 213
4.4. Essential Remarks
In seminal works about money and income (as for instance in Tobin, 1970),
the analysis is restricted in a pure theoretical consideration. Some authors
(see for instance, Friedman and Kuttner, 1992) write many explanations
about co-integration, co-integrating vectors, and error-correction models,
but I did not trace any attempt to compute either. In a later paper by the
same authors (Friedman and Kuttner, 1993), I read (p. 200) the phrase,
“vector autoregression system,” which in fact is understood as a VAR. The
point is that no VAR model is specified in this work. Besides, the lag length
is determined by simply applying the F-test (p. 191). In this context, the
validity of the results is questionable. In other applications (see for instance,
Arestis and Demetriades, 1997), where a VAR model has been formulated,
nothing is mentioned about the test applied to determine the maximum lag
length. Also, in this paper, the authors are restricted to the use of trace
statistic (l (trace) ) to test for co-integration (p. 787), although this is the
necessary but not the sufficient condition, as pointed out above. From other
research works (see for instance, Arestis et al., 2001), I get the impression
that there is not a clear notion regarding stationarity and/or integration,
since the authors state [p. 22 immediately after Eq. (1)], that “D isaset
of I(0) deterministic variables such as constant, trend and dummies. . . ”.
It is clear that this verification is false. How can a trend, for instance, be
a stationary, I(0), variable? 10 The authors declare (p. 24) that “We then
perform co-integration analysis. . . ”. The point is that apart from some
theoretical issues, I did not trace such an analysis in the way it is applied
here. Besides, nothing is mentioned about any ECVAR, analogous to the one
that is formulated and used in this study. Most essentially, I have not traced,
In case that the disequilibrium errors are computed from:
then the co-integration vector will have the form:
u i = Ŷ i − Y i (13)
[−10.289613 0.003621]. (14)
It is noted also that hat (ˆ) is omitted from the disequilibrium errors u i , for avoiding any
confusion with the OLS disturbances.
It should be emphasized that in such a case, i.e., using the disequilibrium errors computed
from Eq. (13), then the sign of the coefficient of adjustment, as will be seen later, will be
changed.
10 It should be re-called at this point, that if t i is a common trend, then t i = 1(∀ i).

214 Athanasios Athanasenas
in relevant works, the stability analysis applied for the system presented
in Eq. (8).
4.5. The ECM Formulation
The lagged values of the disequilibrium errors, that is u i−1 , serve as an
error correction mechanism in a short-run dynamic relationship, where the
additional explanatory variables may appear in lagged first differences. All
variables in this equation, also known as ECM, are stationary so that, from
the econometric point of view, it is a standard single equation model, where
all the classical tests are applicable. It should be noted, that the lag structure
and the details of the ECM, should be in line with the formulation as seen
in Eq. (6a). Hence, I started from this relation considering the errors u i
and estimated the following model, given that the maximum lag length is
p − 1 i.e., 3.
Y i = α 0 +
3∑
α j Y i−j +
j=1
3∑
β j W i−j − a Y u i−1 + Y v i . (15)
j=1
Note that Y v i are the model disturbances. If the adjustment coefficient
a Y is significant, then we may conclude that in the long run, W causes Y.
If a Y = 0, then no such a causality effect exists. In case that all β j are
significant, then there is a causality effect in the short run, from W to
Y. Ifallβ j = 0, then no such causality effect exists. The estimation
results are presented below.
Y i = 0.5132+ 0.2618Y i−1 + 0.161Y i−2 − 0.00432Y i−3 + 0.0273W i−1
(0.125) (0.074) (0.073) (0.0738) (0.075)
p value 0.0001 0.0005 0.0276 0.953 0.719
Hansen 0.0370 0.1380 0.2380 0.234 0.128
+ 0.0487W i−2 − 0.076W i−3 − 0.0879u i−1 + Y ˆv i
(0.075) (0.065) (0.022)
p value 0.519 0.242 0.0001
Hansen 0.065 0.098 0.025 (for all coefficients 2.316) (16)
¯R 2 = 0.167,s= 0.009, DWd = 1.98,F (7,189) = 6.65,
Condition number (CN) = 635.34.
(p value = 0.0)

Credit and Income 215
We observe that the estimated adjustment coefficient (−0.0879) is
significant and almost identical to the (1, 1) element of matrix A, as seen
in Eq. (9), which is computed by the ML method. According to Hansen
statistics, all coefficients seem to be stable for α = 0.05. The BG test
revealed that no autocorrelation problems exist. In models like the one seen
in Eq. (16), the term u i−1 usually produces the smallest Spearman’s correlation
coefficient (r s ). In this particular case, we have: r s =−0.0979,
t =−1.37, p = 0.172, which means that no heteroscedasticity problems
exist. Finally, the RESET test shows that there is no any specification error.
In Eq. (16), we have an inflated CN due to spurious multicollinearity,
which is verified from the revised CN, having the value of 3.42 and
as Lazaridis (2007) has shown, this means that, in fact, there is not any
serious multicollinearity problem, affecting the reliability of the estimation
results. In many applications, particularly when the variables are in logs,
then usually the value of this statistic (CN) is extremely high, which in most
cases, as stated above, is due to the spurious multicollinearity, which can be
revealed by computing the revised CN, which is not widely known and it
seems that this is the main reason, for not reporting this statistic in relevant
applications.
To test the null, H 0 : β 1 = β 2 = β 3 = 0, where β j are the coefficients of
W i−j (j = 1, 2, 3), we computed the F-statistic that is F (3,189) = 0.533
(p- value = 0.66). Hence, the null is accepted, which means that there is not
any short-run causality effect from W to Y, but only in the levels, i.e., in
the long run, W causes Y. Observing the value of the adjustment coefficient
(−0.0879), I may conclude that it gives a satisfactory percentage, regarding
the money income convergence towards a long-run equilibrium. 11
4.6. Dynamic Forecasting with an ECVAR
To complete the ECVAR model, it is necessary to estimate a short-run relation
for W. Thus, we consider an equation which is similar to Eq. (15) i.e.,
W i = b 0 +
3∑
a j Y i−j +
j=1
3∑
b j W i−j − a W u i−1 + W v i . (17)
j=1
11 It is already mentioned that if the disequilibrium errors are computed from Eq. (13),
instead of Eq. (12), then the estimated coefficient of adjustment will have a positive sign.

216 Athanasios Athanasenas
The estimation results are as follows 12 :
W i = 0.2241+ 0.0977Y i−1 + 0.2256Y i−2 + 0.199Y i−3 + 0.4864W i−1
(0.125) (0.0733) (0.072) (0.073) (0.075)
p value 0.075 0.183 0.002 0.0072 0.000
Hansen 0.075 0.181 0.041 0.7130 0.045
+ 0.0123W i−2 + 0.068W i−3 − 0.03852u i−1 + W ˆv i
(0.87) (0.29) (0.0216)
p value 0.519 0.242 0.076
Hansen 0.062 0.181 0.075 (for all coefficients 2.268)
¯R 2 = 0.541, s = 0.009, DWd = 1.97,
F (7,189) = 34.0(p value = 0.0), CN = 635.4, Revised CN = 3.42.
(18)
Presumably, we are on the right way, since the estimated adjustment coefficient
is almost the same as the one computed by the ML method as in
the previous case. This is the (2, 1) element of matrix A as seen in Eq. (9).
Note that this coefficient is significant for α ≥ 0.08, which means that there
is a rather weak causality effect from Y to W in the long run.
To test the null H 0 : a 1 = a 2 = a 3 = 0, where the coefficients
a j (j = 1, 2, 3) as seen in Eq. (17), we compute the relevant F-statistic,
i.e., F (3,189) = 8.42 (p-value = 0.0). This implies that indeed there is a
causality effect in the short run, from Y to W.
Considering the complete ECVAR, i.e., Eqs. (16) and (18), Eq. (10a) is
used to compute the series {u i }, together with some trivial identities, I form
the following system:
Y i = ˆβ 0 +
W i = ˆb 0 +
3∑
ˆα j Y i−j +
j=1
3∑
â j Y i−j +
j=1
3∑
ˆβ j W i−j −â Y u i−1 + Y ˆv i
j=1
3∑
ˆb j W i−j −â W u i−1 + W ˆv i
j=1
12 According to Hansen statistics, all coefficients seem to be stable for α = 0.05.
The Spearman’s correlation coefficient (r s ) regarding the term u i−1 , is: r s = −0.075,
t =−1.051, p = 0.294, which means that we do not have to bother about heteroscedasticity
problems. Also the revised CN indicates that no multicollinearity problems exist, in
order to affect the reliability of the estimation results.

Credit and Income 217
Y i = Y i + Y i−1
W i = W i + W i−1
u i = Y i − 0.289613W i − 0.0036218t i .
(19)
It may be useful to note that there are three identities in the system
and the only exogenous variable present in the system is the trend. We may
obtain dynamic simulation results from the ECVAR specified in Eq. (19),
in order to obtain predictions for Y i and W i and at the same time to verify
the validity of the co-integration vector used. This can be achieved by first
formulating the following deterministic system.
K 0 y i = K 1 y i−1 + K 2 y i−2 + K 3 y i−3 + ˜Dq i (20)
where y i = [ϒ i W i u i Y i W i ] ′ , q i = [t i 1] ′
⎡
K 0 =
⎢
⎣
1 0 0 0 0
0 1 0 0 0
0 0 1 −1 0.289613
−1 0 0 1 0
0 −1 0 0 1
⎤
⎥
⎦ ,
⎡
⎤
0.2618 0.0273 −0.0879 0 0
0.0977 0.4864 −0.03852 0 0
K 1 =
⎢ 0 0 0 0 0
⎥
⎣ 0 0 0 1 0⎦ ,
0 0 0 0 1
⎡
⎤
0.161 0.0487 0 0 0
0.2256 0.0123 0 0 0
K 2 =
⎢ 0 0 0 0 0
⎥
⎣ 0 0 0 0 0⎦ ,
0 0 0 0 0
⎡
⎤
−0.00432 0.076 0 0 0
0.199 −0.068 0 0 0
K 3 =
⎢ 0 0 0 0 0
⎥
⎣ 0 0 0 0 0⎦ ,
0 0 0 0 0

218 Athanasios Athanasenas
and
⎡
˜D =
⎢
⎣
⎤
0 0.5132
0 0.2241
⎥
⎦ .
−0.003621 0
0 0
0 0
Pre-multiplying Eq. (20) by K0 −1 we get:
y i = Q 1 y i−1 + Q 2 y i−2 + Q 3 y i−3 + Dq i (21)
where Q 1 = K0 −1 K 1, Q 2 = K0 −1 K 2, Q 3 = K0 −1 K 3, and D = K0
−1 ˜D.
The system given in Eq. (21) can be transformed to an equivalent firstorder
dynamic system, in a similar way to the one already described earlier
[see Eqs. (8) and (8a)]. It is noted that in this case matrix à is of dimension
(15 × 15). It is important to mention again that we should avoid using
a dynamic system, for simulation purposes, that is unstable. Thus, from
this system, we can obtain dynamic simulation results for the variables Y i
and W i . These results are graphically presented (Fig. 2).
The very low value of Theil’s inequality coefficient U, for both cases
is a pronounced evidence that, apart from computing the indicated cointegration
vector, we have also formulated the suitable ECVAR so that the
results obtained are undoubtfully robust.
5. Conclusions and Implications
The purpose of this study is to contribute to the empirical investigation of
the co-integration dynamics of the credit-income nexus, within the economic
growth process of the post-war US economy, over the period from
1957 to 2007.
Utilizing advanced and contemporary co-integration analysis and
applying vector ECM estimation, we place special emphasis on forecasting
and system stability analysis. I can say that to the best of my knowledge,
similar system stability and forecasting analysis, as the one applied here,
is very difficult to meet in the relevant literature, after taking into consideration
similar research works. See for example, (Arestis and Demetriades,
1997; Arestis et al., 2001; Demetriades and Hussein, 1996; Friedman and
Kuttner, 1992; 1993; Levine and Zervos, 1998; Rousseau and Wachtel,
1998; 2000).
My results state clearly that there is no short-run causality effect from
credit changes to income changes, but only in the levels, that is in the long

Credit and Income 219
Figure 2.
Results of dynamic simulations.

220 Athanasios Athanasenas
run, credit causes money income. From my co-integration analysis, I found
that the adjustment coefficient is significant and its value (−0.0879), gives a
satisfactory percentage, regarding the money income convergence towards
a long-run equilibrium.
Moreover, we observe a causality effect from income changes to credit
changes, in the short run for the post-war US economy. The validity of
the credit view theorists seems rather evident, by taking into account the
contemporary co-integration and system stability approaches.
Further, in terms of reasonable research implications, following our
contemporary co-integration and system stability approaches, we may
stress the need for an in-depth investigation of the credit cycle and fluctuations
in commercial credit standards. 13
References
Angeloni, I, KA Kashyap and B Mojon (2003). Monetary Policy Transmission in the Euro
Area. Part 4, Chap. 24 NY: Cambridge University Press.
Arestis, P and P Demetriades (1997). Financial development and economic growth: assessing
the evidence. The Economic Journal 107, 783–799.
Arestis, P, PO Demetriades and KB Luintel (2001). Financial development and economic
growth: the results of stock markets. Journal of Money, Credit and Banking 33(1),
16–41.
Bernanke, SB (1983). Non-monetary effects of the financial crisis in the propagation of the
great depression. American Economic Review 73(3), 257–276.
Bernanke, SB (1988). Monetary policy transmission: through money or credit? Business
Review, November/December, 3–11 (Federal Reserve Bank of Philadelphia).
Bernanke, SB and SA Blinder (1988). Credit, money, and aggregate demand. The American
Economic Review, Papers and Proceedings 78(2), 435–439.
Bernanke, SB and SA Blinder (1992). The federal funds rate and the channels of monetary
transmission. The American Economic Review 82(4), 901–921.
Bernanke, SB and M Gertler (1995). Inside the black box: the credit channel of monetary
transmission. The Journal of Economic Perspectives 9(4), 27–48.
Bernanke, SB and H James (1991). The gold standard, deflation, and financial crisis in the
great depression: an International comparison. In Financial Markets and Financial
Crises, RG Hubbard (ed.), Chicago: University of Chicago Press for NBER, 33–68.
Brunner, K and HA Meltzer (1988). Money and credit in the monetary transmission process.
American Economic Review 78, 446–451.
Demetriades, PO and K Hussein (1996). Does financial development cause economic
growth? Journal of Development Economics 51, 387–411.
13 See, for example, Lown and Morgan (2006), for parallel research on commercial credit
standards, following “traditional” VAR analysis.

Credit and Income 221
Dickey, DA and WA Fuller (1979). Distribution of the estimators for autoregressive
time series with a unit root. Journal of the American Statistical Association 74,
427–431.
Dickey, DA and WA Fuller (1981). Likelihood ratio statistics for autoregressive time series
with a unit root. Econometrica 49, 1057–1072.
Engle, RF and CWJ Granger (1987). Cointegration and error-correction: representation,
estimation, and testing. Econometrica 55, 251–276.
Friedman, M (1961). The lag in the effect of monetary policy. Journal of Political Economy,
October 69, 447–466.
Friedman, M (1964). The monetary studies of the national bureau. National Bureau of Economic
Research, Annual Report. New York: National Bureau of Economic Research,
1–234.
Friedman, B and KN Kuttner (1992). Money, income, prices and interest rates. The American
Economic Review 82(3), 472–492.
Friedman, B and KN Kuttner (1993). Another look at the evidence of money-income causality.
Journal of Econometrics 57, 189–203.
Friedman, M and A Schwartz (1963). Money and business cycles. Review of Economics and
Statistics, February, (suppl. 45), 32–64.
Gertler, M and S Gilchrist (1993). The role of credit market imperfections in the monetary
transmission mechanism: arguments and evidence. Scandinavian Journal of Economics
95(1), 43–64.
Goldsmith, RW (1969). Financial structure and development. New Haven, CT: Yale
University Press.
Granger, CWJ and P Newbold (1974). Spurious regressions in econometric model specification.
Journal of Econometrics 2, 111–120.
Hamilton, JD (1994). Time Series Analysis. Princeton: Princeton University Press.
Harris, R (1995). Using Cointegration Analysis in Econometric Modeling. London: Prentice
Hall.
Holden, D and R Perman (1994). Unit roots and cointegration for the economists. In Cointegration
for the Applied Economist, BB Rao (Ed.), UK: St. Martin’s Press, 47–112.
Johansen, S (1995). Likelihood-Based Inference in Cointegrating Vector Autoregressive
Models. New York: Oxford University Press.
Johansen, S and K Juselius (1990). Maximum likelihood estimation and inference on cointegration
with application to the demand for money. Oxford Bulletin of Economics and
Statistics 52, 169–210.
Kashyap, KA and CJ Stein (1994). Monetary policy and bank lending. NBER Studies in
Business Cycles 29, 221–256.
Kashyap, KA and CJ Stein (2000). What do a million observations on banks say about the
transmission of monetary policy? The American Economic Review 90(3), 407–428.
Kashyap, KA, AO Lamont and CJ Stein (1994). Credit conditions and the cyclical behavior
of inventories. The Quarterly Journal of Economics 109(3), 565–592.
King, GR and R Levine (1993). Finance, entrepreneurship and growth: theory and evidence.
Journal of Monetary Economics 32, 1–30.
Lazaridis, A (2007). A note regarding the condition number: the case of spurious and latent
multicollinearity. Quality & Quantity 41(1), 123–135.
Levine, R and S Zervos (1998). Stock markets, banks, and economic growth. American
Economic Review 88, 537–558.

222 Athanasios Athanasenas
Lown, C and DP Morgan (2006). The credit cycle and the business cycle: new findings
using the loan officer opinion survey. Journal of Money, Credit, and Banking 38(6),
1575–1597.
MacKinnon, J (1991). Critical values for co-integration tests. In Long-Run Economic Relationships,
RF Engle and CWJ Granger (eds.), pp. 267–276. Oxford: Oxford University
Press.
Mckinnon, RL (1973). Money and Capital in Economic Development. Washington, DC:
Brookings Institution.
Meltzer, HA (1995). Monetary, credit and (other) transmission processes: a monetarist perspective.
The Journal of Economic Perspectives 9(4), 49–72.
Mishkin, SF (1995). Symposium on the monetary transmission mechanism. The Journal of
Economic Perspectives 9(4), 3–10.
Mouza, AM and D Paschaloudis (2007). Advertisement and sales: a contemporary cointegration
analysis. Journal of Academy of Business and Economics 7(2), 83–95.
Murdock, K and J Stiglitz (1997). Financial restraint: towards a new paradigm. Journal of
Monetary Economics 35, 275–301.
Rousseau, PL and P Wachtel (1998). Financial intermediation and economic performance:
historical evidence from five industrialized countries. Journal of Money, Credit and
Banking 30, 657–678.
Rousseau, PL and P Wachtel (2000). Equity markets and growth: cross-country evidence on
timing and outcomes, 1980–1995. Journal of Banking and Finance 24, 1933–1957.
Shaw, ES (1973). Financial Deepening in Economic Development. New York: Oxford
University Press.
Sims, CA (1972). Money, income, and causality. The American Economic Review 62(4),
540–552.
Sims, CA (1980a). Comparison of interwar and postwar business cycles. The American
Economic Review 70, 250–277.
Sims, CA (1980b). Macroeconomics and reality. Econometrica 48, 1–48.
Stiglitz, EJ (1992). Capital markets and economic fluctuations in capitalist economies.
European Economic Review 36, 269–306.
Stock, JM and MW Watson (1988). Testing for common trends. Journal of the American
Statistical Association 83, 1097–1107.
Stock, J and MW Watson (1989). Interpreting the evidence on money-output causality.
Journal of Econometrics, January, 161–181.
Swanson, N (1998). Money and output viewed through rolling window. Journal of Monetary
Economics 41, 455–473.
Tobin, J (1970). Money and income: post hoc ergo propter hoc? Quarterly Journal of
Economics 84, 301–329.
Trautwein, M (2000). The credit view, old and new. Journal of Economic Surveys 14(2)
155–189.

INDEX
adaptive control, 44, 49, 57, 59
asymptotic co-variance, 46
autocorrelation, 35, 36, 40, 182, 184, 185,
187, 188, 191, 212, 215
automatic stabilizer, 70, 71, 74, 76, 79, 80,
96, 98
balance of payments, 44, 49, 53
bank credit, 202–205
Bank of England, 69, 70, 74, 76–78, 90
British fiscal policy, 69, 73, 81
budget stability, 74
business cycle, 9, 202
cash-balance, 52
causality, 201, 202, 204, 205, 214–216,
218, 220
Central Bank objective function, 85
Cholesky’s factorization, 24
Chow stability, 184
co-integration, 23, 25, 28–32, 34, 41, 201,
204–206, 208, 209, 212, 213, 217, 218,
220
collectivism, 143
conformability, 26, 208
conformity, 140, 143
corporate culture, 139, 145
credit and income, 201, 204
credit demand, 202, 203
critical value, 30, 33, 38–40, 188, 189, 212
current deficits, 79, 83
CUSUM, 185, 186, 188–191
cyclical stability, 74
Czech Republic, 173–177, 181–183,
189–193, 196, 197, 199
debt ratio, 72, 78, 92, 96, 99
decision orientation, 132
decomposition, 26, 27
dependent central bank, 88, 90, 94
depression, 9, 202, 203
deterministic, 25, 41, 209, 212, 213, 217
devaluation, 57, 176, 177
diagnostic, 185–188, 191, 197
Dickey–Fuller tests, 30, 206
discount rate, 52, 57–59
discretionary fiscal policy, 82
discretionary tax revenues, 82
disequilibrium, 25, 28, 208, 212–215
domestic absorption, 49, 50, 53, 59
dynamic response multiplier, 57
Eastern European Countries, 173
econometrics, 6, 9, 204
ECVAR, 23, 25, 201, 204, 206–209, 213,
215–218
Eigen values, 24–26, 211
emissions, 101, 103–106
enterprise integration, 121, 125–128
enterprise integration modeling, 121
enterprise modeling, 121–124, 132
environmental economics, 101–103
environmental taxation, 101, 103
ERM, 176, 193
error co-variance matrix, 48
error-correction, 23, 201, 205, 213, 214
European Commission, 69, 79, 98
Eurozone, 69, 72, 77–81, 88, 93–95
ex-ante responses, 76
exchange rate, 50, 53, 58, 60, 74,
173–178, 180–183, 185, 187–193, 197
exclusivity, 143
feasibility region, 3, 5
feasible set, 16
feedback rule, 77
223

224 Index
fiscal expansions, 91, 92
fiscal leadership, 69, 71, 73, 76–78, 81,
85, 89–97, 99
fixed parity, 176
function oriented enterprise, 128
functional entities, 122–124, 126
fund-bank adjustment policy model, 49
Gaussian, 44, 62
Germany, 93, 94, 99, 174, 176, 181–187,
190, 194, 197
goal programming, 151, 155, 156, 161,
168
Hamiltonian, 111
health care unit, 168
health service management, 151
heteroscedasticity, 35, 37, 39, 184, 185,
194, 212, 215, 216
Hou-Ren-Sou, 140, 143, 144
human resources practices, 130, 142, 144
human ware, 141
hybrid modeling constructs, 130
imitation-type dynamics, 103, 106
independent monetary policies, 71, 75
Indian economy, 49, 50
inflation, 69, 70, 72–74, 76–80, 82, 84, 85,
88–96, 99, 153, 164, 173–179,
181–183, 185–193
inflation control, 70, 73, 79, 92, 173, 174,
176, 177, 191, 192
input-output, 6–9, 11, 12, 14
institutional parameters, 76, 86, 96
integration challenges, 121
inter-temporal optimization problem, 107
interactive voice response, 153
interest rate, 38, 50–52, 57–60, 75, 77–81,
176, 178, 179, 181, 191, 192
Japanese national culture, 137, 139, 140,
147
Japanese Organizational culture and
corporate performance, 137
Jaque-Bera criterion, 29
just in time, 144
Kaizen, 140–142
Kroneker product, 46
leadership, 69–73, 76–79, 81, 85, 86,
89–97, 99, 103, 130, 137, 139, 142,
144, 145
lean production system, 141, 142
linear constraints, 3, 10
linear programming, 3, 4, 6–8, 10, 14
liquidity, 203
LISREL, 145
Maastricht criteria, 173, 176, 177
macro values, 138, 143
management support, 131
mathematical programming, 3, 156
maximization, 7, 82, 112, 151
maximum likelihood, 24, 49, 205
meso values, 138
meta-analysis, 117
micro values, 138, 143
minimum variance, 25, 31–33, 41
ML method, 24, 25, 28, 31, 32, 34, 40,
208, 211, 215, 216
modeling method, 124
monetary and fiscal policy, 43, 44, 49, 53,
56–59, 82, 84, 93
monetary policy, 43, 44, 49, 53, 56–59,
69–82, 84, 85, 91–95, 98, 102, 103,
173, 174, 176, 178, 179, 185, 186, 188,
190, 192, 202–204
multicollinearity, 215, 216
multi functional team, 142
multiple equilibria, 101, 112, 113
Nash equilibrium, 81
Nash solution, 70, 102, 107, 110
New Cambridge model, 50
new constraint, 161, 162
new credit, 202
non-believers, 103, 105–107, 117
object request brokers, 126
old credit, 202
OLS, 23, 25, 28–32, 183, 184, 213
optimal control, 45, 46, 50, 55

Index 225
optimal currency area, 175
optimization, 3, 4, 7, 16, 44, 49, 91, 107,
110–112
organizational culture, 130, 137–139, 142,
144
output gap, 72, 77–82, 179–183, 187, 189,
191
Pareto-improvement, 110
Pareto-inferior, 116
Phillips curve, 87, 98, 178
Poland, 173–177, 181, 182, 185, 187, 188,
190–193, 195, 197, 198
primary deficit, 72, 79
pro-cyclicality, 85, 87
product modeling, 122
productivity, 175
pseudo-inverse, 26
public sector deficit, 84
quadratic function, 10
quality circle, 141
rational expectations, 44, 86, 179
reduced form, 44, 46, 48, 58, 59, 82, 84,
179
reduced form coefficients, 44, 46, 48
regulator, 76, 101–111, 113–117
regulator’s trustworthiness, 115
residuals, 24, 30, 35, 36, 39, 54, 179, 184,
185, 187, 188, 191, 194
resource information, 122
Ricatti-equations, 45
robustness, 55
sequential Nash game, 103, 107
short-run stabilization, 70, 76, 80
simplex algorithm, 6, 15
singular value, 26–28, 31, 33
Skiba point, 112, 115, 116
Slovenia, 173–177, 181–183, 185,
190–193, 196, 197, 200
stability, 11, 54, 55, 57, 74, 76, 80–84, 95,
113, 144, 176, 178, 184, 185, 191, 193,
201, 202, 204–206, 210, 211, 214, 218,
220
stabilization policy, 43, 71
standard deviation, 30, 32–34
state variable form, 49, 50
statically optimal, 109, 113
steady-state, 82, 83
structural deficit, 79, 80
structural model, 44, 49, 178
symmetric stabilization, 75
tax revenue, 50, 51, 57, 58, 60, 82, 83, 95,
96, 104, 106
Theil’s inequality, 206, 218
time varying responses, 43
time-invariant econometric model, 47
time-varying model, 44, 47
TQM, 141, 142, 144
transition, 45, 50, 54, 173–176, 178–180,
185, 186, 188, 189, 191, 192
transmission of monetary policy, 173, 178,
179, 190, 192, 203
UK government, 69
underutilization, 158, 160
unstable middle equilibrium, 115
updating method, 44, 46
US economy, 201, 202, 204, 218, 220
VAR, 23, 25, 27, 28, 32, 44, 178, 201, 205,
207, 213, 220